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Appendix C Answers to Exercises

I Linear Equations and Lines
1 Variables, Expressions, Equations, and Inequalities
1.1 Variables and Evaluating Expressions
1.1.6 Exercises

Skills Practice

1.1.6.1.
1.1.6.1.a
Answer 1.
\(d\hbox{, }D\hbox{, }x\hbox{, or }y\)
Answer 2.
\({\text{feet}}\)
1.1.6.1.b
Answer 1.
\(w\hbox{, }W\hbox{, }x\hbox{, or }y\)
Answer 2.
\({\text{pounds}}\)
1.1.6.3.
Answer.
\(5\)
1.1.6.5.
Answer.
\(4\)
1.1.6.7.
Answer.
\(1\)
1.1.6.9.
Answer.
\(-9\)
1.1.6.11.
Answer.
\(11\)
1.1.6.13.
Answer.
\(66\)
1.1.6.15.
Answer.
\(-34\)
1.1.6.17.
1.1.6.17.a
Answer.
\(16\)
1.1.6.17.b
Answer.
\(81\)
1.1.6.19.
1.1.6.19.a
Answer.
\(-36\)
1.1.6.19.b
Answer.
\(-64\)
1.1.6.21.
1.1.6.21.a
Answer.
\(729\)
1.1.6.21.b
Answer.
\(-216\)
1.1.6.23.
1.1.6.23.a
Answer.
\(324\)
1.1.6.23.b
Answer.
\(108\)
1.1.6.25.
Answer.
\(60\)
1.1.6.27.
Answer.
\(33\)
1.1.6.29.
Answer.
\(4 {\textstyle\frac{1}{2}}\)
1.1.6.31.
Answer.
\(3\)
1.1.6.33.
Answer.
\(-4\)
1.1.6.35.
Answer.
\(-3\)
1.1.6.37.
Answer.
\(-90\)
1.1.6.39.
Answer.
\(-130\)
1.1.6.41.
Answer.
\(81\)
1.1.6.43.
Answer.
\(5832\)
1.1.6.45.
Answer.
\(15\)
1.1.6.47.
Answer.
\(-65\)
1.1.6.49.
Answer.
\(17\)
1.1.6.51.
Answer.
\(-75\)
1.1.6.53.
Answer.
\(-4\)
1.1.6.55.
Answer.
\(10\)

Applications

1.1.6.57.
Answer.
\(280\ {\rm degK}\)
1.1.6.59.
Answer.
\(174\ {\rm years}\)
1.1.6.61.
Answer.
\(204\ {\rm mi}\)
1.1.6.63.
Answer.
\(75600\ {\rm seconds}\)
1.1.6.65.
Answer.
\(37.4\ {\rm degF}\)
1.1.6.67.
Answer.
\(111\ {\rm bpm}\)
1.1.6.69.
Answer.
\(30.3\%\)
1.1.6.71.
Answer.
\(99\ {\rm ft}\)
1.1.6.73.
Answer.
\(129.766\ {\rm feet}\)
1.1.6.75.
Answer.
\(3.42208\ {\rm seconds}\)
1.1.6.77.
Answer.
\(32.2\%\)
1.1.6.79.
Answer.
\(26\)
1.1.6.81.
1.1.6.81.a
Answer.
\(4.4\ {\rm ft}\)
1.1.6.81.b
Answer.
\(5.2\ {\rm ft}\)
1.1.6.83.
Answer.
\(60x\)
1.1.6.85.
Answer.
\(1.8x\)
1.1.6.87.
Answer.
\(n+5\)
1.1.6.89.
Answer.
\(360+125n\)

1.2 Combining Like Terms
1.2.5 Exercises

Prerequisite/Review Skills

1.2.5.1.
Answer.
\({\frac{22}{17}}\)
1.2.5.3.
Answer.
\({\frac{4}{17}}\)
1.2.5.5.
Answer.
\({\frac{11}{8}}\)
1.2.5.7.
Answer.
\({\frac{1}{6}}\)
1.2.5.9.
Answer.
\({\frac{81}{11}}\)
1.2.5.11.
Answer.
\({\frac{3}{10}}\)
1.2.5.13.
Answer.
\({\frac{83}{182}}\)
1.2.5.15.
Answer.
\({\frac{1}{12}}\)
1.2.5.17.
Answer.
\({\frac{61}{63}}\)
1.2.5.19.
Answer.
\({\frac{13}{40}}\)
1.2.5.21.
Answer.
\({\frac{2}{3}}\)
1.2.5.23.
Answer.
\({\frac{1}{3}}\)
1.2.5.25.
Answer.
\({\frac{79}{60}}\)
1.2.5.27.
Answer.
\({\frac{58}{63}}\)
1.2.5.29.
Answer.
\({\frac{47}{126}}\)
1.2.5.31.
Answer.
\({\frac{2}{35}}\)

Skills Practice

1.2.5.33.
Answer.
\(-{\frac{1}{2}}u, t, 2.7D, 18b\)
1.2.5.35.
Answer.
\({\frac{3}{10}}J, -13k, 49J\)
1.2.5.37.
Answer.
\({\frac{1}{10}}, 77x^{5}, -x^{9}\)
1.2.5.39.
Answer.
\(5.5y^{8}, -y^{9}, y^{9}\)
1.2.5.41.
Answer.
\(18.2K\)
1.2.5.43.
Answer.
\(\frac{6}{5}X\)
1.2.5.45.
Answer.
\(8.1i-l\)
1.2.5.47.
Answer.
\(-10u+4u^{3}+\frac{8}{3}u^{4}\)
1.2.5.49.
Answer.
\(\frac{-31}{6}F+\frac{1}{2}R\)
1.2.5.51.
Answer.
\(34R+6.8g\)
1.2.5.53.
Answer.
\(\frac{49}{36}c^{2}-2c^{5}\)
1.2.5.55.
Answer.
\(0.6n^{4}+14.9n^{6}\)
1.2.5.57.
Answer.
\(-9z\)
1.2.5.59.
Answer.
\(-3.9K\)
1.2.5.61.
Answer.
\(\frac{11}{3}W+\frac{29}{10}H\)
1.2.5.63.
Answer.
\(-6.3h+10.5Y\)
1.2.5.65.
Answer.
\(-71.2t^{2}+1.3t^{6}\)
1.2.5.67.
Answer.
\(\frac{88}{21}E^{3}+\frac{2}{5}E^{5}\)

Applications

1.2.5.69.
Answer.
\(\frac{53}{12}Q+\frac{9}{4}U\)
1.2.5.71.
Answer.
\(6.9c+81.3k\)
1.2.5.73.
Answer.
\(\frac{37}{8}n+\frac{19}{6}z+2c\)
1.2.5.75. Office Lunch.
1.2.5.75.a
Answer.
\(14S+8B\)
1.2.5.75.b
Answer.
\(27S+18B\)
1.2.5.77. Sportsball.
1.2.5.77.a
Answer.
\(19P+36L+44S\)
1.2.5.77.b
Answer.
\(25P+60L+81S\)

1.3 Comparison Symbols and Notation for Intervals
1.3.4 Exercises

Prerequisite/Review Skills

1.3.4.1.
Answer.
\(2.2\)
1.3.4.3.
Answer.
\(7.25\)
1.3.4.5.
Answer.
\(4.875\)
1.3.4.7.
Answer.
\(0.05\)
1.3.4.9.
Answer.
\(3.33333\)
1.3.4.11.
Answer.
\(5.83333\)
1.3.4.13.
Answer.
\(1.54545\)
1.3.4.15.
Answer.
\(4.58333\)

Skills Practice

1.3.4.17.
Answer.
\(\text{False}\)
1.3.4.19.
Answer.
\(\text{False}\)
1.3.4.21.
Answer.
\(\text{False}\)
1.3.4.23.
Answer.
\(\text{True}\)
1.3.4.25.
Answer.
\(\text{True}\)
1.3.4.27.
Answer.
\({\verb!<!}\)
1.3.4.29.
Answer.
\({\verb!>!}\)
1.3.4.31.
Answer.
\({\verb!<!}\)
1.3.4.33.
Answer.
\({\text{=}}\)
1.3.4.35.
Answer.
\({\verb!<!}\)
1.3.4.37.
Answer.
\(9>6>0>-3>-6\)
1.3.4.39.
Answer.
\(8.9>1.8>-0.7>-4.9>-5.8\)
1.3.4.41.
Answer.
\({\frac{10}{7}}>{\frac{11}{8}}>{\frac{7}{6}}>{\frac{1}{2}}>{\frac{2}{9}}\)
1.3.4.43.
Answer.
\({\frac{8}{13}}>0.3>\sqrt{3}>\frac{\pi }{4}>5\)
1.3.4.45.
Answer 1.
\(\left\{x \mid x < -4\right\}\)
Answer 2.
\(\left(-\infty ,-4\right)\)
1.3.4.47.
Answer 1.
\(\left\{x \mid x\le -1\right\}\)
Answer 2.
\(\left(-\infty ,-1\right]\)
1.3.4.49.
Answer 1.
\(\left\{x \mid x\ge 3\right\}\)
Answer 2.
\(\left[3,\infty \right)\)
1.3.4.51.
Answer 1.
\(\left\{x \mid x > 6\right\}\)
Answer 2.
\(\left(6,\infty \right)\)
1.3.4.53.
Answer 1.
\(\left\{\text{interval}, \left[-6,\infty \right)\right\}\)
Answer 2.
\(\left[-6,\infty \right)\)
1.3.4.55.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-2\right)\right\}\)
Answer 2.
\(\left(-\infty ,-2\right)\)
1.3.4.57.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,1\right]\right\}\)
Answer 2.
\(\left(-\infty ,1\right]\)
1.3.4.59.
Answer 1.
\(\left\{\text{interval}, \left(4,\infty \right)\right\}\)
Answer 2.
\(\left(4,\infty \right)\)
1.3.4.61.
Answer 1.
\(\left\{\text{interval}, \left[-7,\infty \right)\right\}\)
Answer 2.
\(\left\{x \mid x\ge -7\right\}\)
1.3.4.63.
Answer 1.
\(\left\{\text{interval}, \left(-4,\infty \right)\right\}\)
Answer 2.
\(\left\{x \mid x > -4\right\}\)
1.3.4.65.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-1\right)\right\}\)
Answer 2.
\(\left\{x \mid x < -1\right\}\)
1.3.4.67.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,3\right]\right\}\)
Answer 2.
\(\left\{x \mid x\le 3\right\}\)

Applications

1.3.4.69.
Answer 1.
\(\left\{a \mid a\ge 21\right\}\)
Answer 2.
\(\left[21,\infty \right)\)
1.3.4.71.
Answer 1.
\(\left\{d \mid d\ge 5000\right\}\)
Answer 2.
\(\left[5000,\infty \right)\)
1.3.4.73.
Answer 1.
\(\left\{\mathrm{pH} \mid \mathrm{pH} < 7\right\}\)
Answer 2.
\(\left(-\infty ,7\right)\)

Challenge

1.3.4.75.
Answer 1.
\({\verb!<!}\)
Answer 2.
\({\verb!>!}\)
Answer 3.
\({\verb!<!}\)
Answer 4.
\({\verb!>!}\)

1.4 Equations, Inequalities, and Solutions
1.4.6 Exercises

Prerequisite/Review Skills

1.4.6.1.
Answer.
\(0\)
1.4.6.3.
Answer.
\({\frac{2}{9}}\)
1.4.6.5.
Answer.
\(45\)
1.4.6.7.
Answer.
\(67\)

Skills Practice

1.4.6.9.
Answer 1.
\(6\)
Answer 2.
\(\text{Yes, it is a solution.}\)
1.4.6.11.
Answer 1.
\(-57.4\)
Answer 2.
\(\text{No, it is not a solution.}\)
1.4.6.13.
Answer 1.
\({\frac{14}{3}}\)
Answer 2.
\(\text{Yes, it is a solution.}\)
1.4.6.15.
Answer 1.
\(-2\)
Answer 2.
\(3\)
Answer 3.
\(\text{No, it is not a solution.}\)
1.4.6.17.
Answer 1.
\({\frac{23}{5}}\)
Answer 2.
\({\frac{189}{40}}\)
Answer 3.
\(\text{No, it is not a solution.}\)
1.4.6.19.
Answer 1.
\(0\)
Answer 2.
\(\text{No, it is not a solution.}\)
1.4.6.21.
Answer 1.
\(42\)
Answer 2.
\(42\)
Answer 3.
\(\text{Yes, it is a solution.}\)
1.4.6.23.
Answer 1.
\(0\)
Answer 2.
\(\text{Yes, it is a solution.}\)
1.4.6.25.
Answer 1.
\(3\)
Answer 2.
\(6\)
Answer 3.
\(\text{No, it is not a solution.}\)
1.4.6.27.
Answer 1.
\(8\)
Answer 2.
\(8\)
Answer 3.
\(\text{Yes, it is a solution.}\)
1.4.6.29.
Answer 1.
\(32\)
Answer 2.
\(\text{No, it is not a solution.}\)
1.4.6.31.
Answer 1.
\(6\)
Answer 2.
\(14\)
Answer 3.
\(\text{No, it is not a solution.}\)
1.4.6.33.
Answer 1.
\({\frac{257}{56}}\)
Answer 2.
\({\frac{257}{56}}\)
Answer 3.
\(\text{Yes, it is a solution.}\)
1.4.6.35.
Answer 1.
\(18\)
Answer 2.
\(\text{No, it is not a solution.}\)
1.4.6.37.
Answer 1.
\(68.1\)
Answer 2.
\(\text{Yes, it is a solution.}\)
1.4.6.39.
Answer 1.
\({\frac{116}{45}}\)
Answer 2.
\(\text{No, it is not a solution.}\)
1.4.6.41.
Answer 1.
\(-18\)
Answer 2.
\(-18\)
Answer 3.
\(\text{Yes, it is a solution.}\)
1.4.6.43.
Answer 1.
\({\frac{38}{3}}\)
Answer 2.
\({\frac{38}{3}}\)
Answer 3.
\(\text{Yes, it is a solution.}\)
1.4.6.45.
Answer 1.
\(8\)
Answer 2.
\(\text{Yes, it is a solution.}\)
1.4.6.47.
Answer 1.
\(5\)
Answer 2.
\(5\)
Answer 3.
\(\text{Yes, it is a solution.}\)
1.4.6.49.
Answer 1.
\(0\)
Answer 2.
\(\text{Yes, it is a solution.}\)
1.4.6.51.
Answer 1.
\(6\)
Answer 2.
\(6\)
Answer 3.
\(\text{No, it is not a solution.}\)
1.4.6.53.
Answer 1.
\(8\)
Answer 2.
\(8\)
Answer 3.
\(\text{No, it is not a solution.}\)
1.4.6.55.
Answer 1.
\(15\)
Answer 2.
\(\text{No, it is not a solution.}\)
1.4.6.57.
Answer 1.
\(8.7\)
Answer 2.
\(8.7\)
Answer 3.
\(\text{No, it is not a solution.}\)
1.4.6.59.
Answer 1.
\({\frac{11}{3}}\)
Answer 2.
\({\frac{11}{3}}\)
Answer 3.
\(\text{Yes, it is a solution.}\)
1.4.6.61.
Answer.
\(\text{Choice 2, Choice 4, Choice 5}\)
1.4.6.63.
Answer.
\(\text{Choice 2, Choice 6}\)
1.4.6.65.
Answer.
\(\text{Choice 4, Choice 6}\)

Applications

1.4.6.67.
Answer 1.
\(55.56\)
Answer 2.
\(\text{Yes, it is a solution.}\)
1.4.6.69.
Answer 1.
\(696\)
Answer 2.
\(\text{Yes, it is a solution.}\)
1.4.6.71.
Answer 1.
\(22\)
Answer 2.
\(\text{Yes, it is a solution.}\)
1.4.6.73.
Answer 1.
\(1225\)
Answer 2.
\(1225\)
Answer 3.
\(\text{Yes, it is a solution.}\)
1.4.6.75.
Answer 1.
\(\frac{1}{294}\pi \)
Answer 2.
\(\text{Yes, it is a solution.}\)

1.5 Solving One-Step Equations
1.5.6 Exercises

Review and Warmup

1.5.6.1.
Answer.
\({\frac{10}{81}}\)
1.5.6.3.
Answer.
\({\frac{32}{81}}\)
1.5.6.5.
Answer.
\({\frac{63}{2}}\)
1.5.6.7.
Answer.
\({\frac{32}{7}}\)
1.5.6.9.
Answer.
\({\frac{23}{19}}\)
1.5.6.11.
Answer.
\({\frac{1}{3}}\)
1.5.6.13.
Answer.
\({\frac{31}{12}}\)
1.5.6.15.
Answer.
\({\frac{295}{234}}\)
1.5.6.17.
Answer.
\({\frac{69}{88}}\)
1.5.6.19.
Answer.
\({\frac{55}{36}}\)
1.5.6.21.
Answer.
\({\frac{5}{63}}\)

Skills Practice

1.5.6.23.
Answer.
\(\left\{-17\right\}\)
1.5.6.25.
Answer.
\(\left\{18\right\}\)
1.5.6.27.
Answer.
\(\left\{-9\right\}\)
1.5.6.29.
Answer.
\(\left\{168\right\}\)
1.5.6.31.
Answer.
\(\left\{-4\right\}\)
1.5.6.33.
Answer.
\(\left\{\frac{10}{11}\right\}\)
1.5.6.35.
Answer.
\(\left\{-3\right\}\)
1.5.6.37.
Answer.
\(\left\{162\right\}\)
1.5.6.39.
Answer.
\(\left\{\frac{31}{12}\right\}\)
1.5.6.41.
Answer.
\(\left\{\frac{-59}{28}\right\}\)
1.5.6.43.
Answer.
\(\left\{\frac{31}{6}\right\}\)
1.5.6.45.
Answer.
\(\left\{\frac{-21}{4}\right\}\)
1.5.6.47.
Answer.
\(\left\{\frac{4}{7}\right\}\)
1.5.6.49.
Answer.
\(\left\{\frac{-36}{35}\right\}\)
1.5.6.51.
Answer.
\(\left\{-18.1\right\}\)
1.5.6.53.
Answer.
\(\left\{-21.57\right\}\)
1.5.6.55.
Answer.
\(\left\{23.03\right\}\)
1.5.6.57.
Answer.
\(\left\{-28.08\right\}\)
1.5.6.59.
Answer.
\(\left\{-0.652174\right\}\)

Applications

1.5.6.61.
Answer 1.
\(74 = C+273\)
Answer 2.
\(-199\ {\rm degC}\)
1.5.6.63.
Answer 1.
\(8.625+N = 17.5\)
Answer 2.
\(8.875\ {\rm in}\)
1.5.6.65.
Answer 1.
\(s\cdot 0.8 = 7\)
Answer 2.
\(\$8.75\)
1.5.6.67.
Answer 1.
\(10\pi = \pi d\)
Answer 2.
\(10\ {\rm cm}\)
1.5.6.69.
Answer 1.
\(-449.44+5.3v+6 = 0\)
Answer 2.
\(83.6679\ {\textstyle\frac{\rm\mathstrut ft}{\rm\mathstrut s}}\)

Challenge

1.5.6.71.
Answer.
\(x+1=6\)

1.6 Solving One-Step Inequalities
1.6.4 Exercises

Skills Practice

1.6.4.1.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-2\right]\right\}\)
Answer 2.
\(\left(-\infty ,-2\right]\)
Answer 3.
\(\left\{u \mid u\le -2\right\}\)
1.6.4.3.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,2\right)\right\}\)
Answer 2.
\(\left(-\infty ,2\right)\)
Answer 3.
\(\left\{E \mid E < 2\right\}\)
1.6.4.5.
Answer 1.
\(\left\{\text{interval}, \left(5,\infty \right)\right\}\)
Answer 2.
\(\left(5,\infty \right)\)
Answer 3.
\(\left\{Q \mid Q > 5\right\}\)
1.6.4.7.
Answer 1.
\(\left\{\text{interval}, \left[-4,\infty \right)\right\}\)
Answer 2.
\(\left[-4,\infty \right)\)
Answer 3.
\(\left\{c \mid c\ge -4\right\}\)
1.6.4.9.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-8\right)\right\}\)
Answer 2.
\(\left(-\infty ,-8\right)\)
Answer 3.
\(\left\{n \mid n < -8\right\}\)
1.6.4.11.
Answer 1.
\(\left\{\text{interval}, \left(12,\infty \right)\right\}\)
Answer 2.
\(\left(12,\infty \right)\)
Answer 3.
\(\left\{z \mid z > 12\right\}\)
1.6.4.13.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-5\right)\right\}\)
Answer 2.
\(\left(-\infty ,-5\right)\)
Answer 3.
\(\left\{K \mid K < -5\right\}\)
1.6.4.15.
Answer 1.
\(\left\{\text{interval}, \left(-1,\infty \right)\right\}\)
Answer 2.
\(\left(-1,\infty \right)\)
Answer 3.
\(\left\{X \mid X > -1\right\}\)
1.6.4.17.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,4\right)\right\}\)
Answer 2.
\(\left(-\infty ,4\right)\)
Answer 3.
\(\left\{h \mid h < 4\right\}\)
1.6.4.19.
Answer 1.
\(\left\{\text{interval}, \left[-6,\infty \right)\right\}\)
Answer 2.
\(\left[-6,\infty \right)\)
Answer 3.
\(\left\{t \mid t\ge -6\right\}\)

1.7 Algebraic Properties and Simplifying Expressions
1.7.6 Exercises

Vocabulary

1.7.6.1.
Answer.
\(9\)
1.7.6.3.
Answer.
\(-{\frac{1}{5}}\)
1.7.6.5.
Answer.
\(0.4\)
1.7.6.7.
Answer.
\({\frac{8}{7}}\)
1.7.6.9.
Answer.
\(-{\frac{3}{2}}\)
1.7.6.11.
Answer.
\(0\)

Skills Practice

1.7.6.13.
Answer.
\(P+\left(21+t\right)\)
1.7.6.15.
Answer.
\(\left(E+E^{2}\right)+{\frac{1}{7}}\)
1.7.6.17.
Answer.
\(18\mathopen{}\left(Qu\right)\)
1.7.6.19.
Answer.
\(K+b\)
1.7.6.21.
Answer.
\(a+{\frac{5}{8}}m\)
1.7.6.23.
Answer.
\(qy+t\)
1.7.6.25.
Answer.
\(\left(J+3\right)\cdot 7\)
1.7.6.27.
Answer.
\(10\mathopen{}\left(2+W\right)\)
1.7.6.29.
Answer.
\(4h+4\cdot 9\)
1.7.6.31.
Answer.
\(6t-6\cdot 8\)
1.7.6.33.
Answer.
\(\frac{9}{5}D+\frac{9}{5}\frac{7}{2}\)
1.7.6.35.
Answer.
\(-P-\left(\frac{3}{5}\right)\)
1.7.6.37.
Answer.
\(13x\)
1.7.6.39.
Answer.
\(\frac{5}{9}x\)
1.7.6.41.
Answer.
\(17y+21\)
1.7.6.43.
Answer.
\(23J+6\)
1.7.6.45.
Answer.
\(35W+52\)
1.7.6.47.
Answer.
\(36g+\left(-21\right)\)
1.7.6.49.
Answer.
\(42s+73\)
1.7.6.51.
Answer.
\(-23D+38\)
1.7.6.53.
Answer.
\(60P+39\)
1.7.6.55.
Answer.
\(17b+22\)
1.7.6.57.
Answer.
\(\frac{146}{3}B+\frac{-56}{5}\)
1.7.6.59.
Answer.
\(26.06y+\left(-54.62\right)\)

Critical Thinking

1.7.6.61.
1.7.6.61.a
Answer.
\(\left(I+f\right)+l\)
1.7.6.61.b
Answer.
\(I+\left(f+l\right)\)

1.8 Modeling with Equations and Inequalities
1.8.6 Exercises

Review and Warmup

1.8.6.1.
1.8.6.1.a
Answer 1.
\(a\hbox{, }A\hbox{, }x\hbox{, }y\hbox{, or }z\)
Answer 2.
\({\verb!ft^2 or m^2!}\)
1.8.6.1.b
Answer 1.
\(a\hbox{, }A\hbox{, }x\hbox{, }y\hbox{, or }z\)
Answer 2.
\({\text{years or months}}\)
1.8.6.1.c
Answer 1.
\(t\hbox{, }T\hbox{, }x\hbox{, }y\hbox{, or }z\)
Answer 2.
\({\text{hours or minutes}}\)

Skills Practice

1.8.6.3.
Answer.
\(x+8\)
1.8.6.5.
Answer.
\(1+x\)
1.8.6.7.
Answer.
\(x-3\)
1.8.6.9.
Answer.
\(5-x\)
1.8.6.11.
Answer.
\(11x+14\)
1.8.6.13.
Answer.
\(14\mathopen{}\left(x+4\right)\)
1.8.6.15.
Answer.
\(8x-3\)
1.8.6.17.
Answer.
\(\frac{x}{12}-6\)
1.8.6.19.
Answer.
\({\frac{9}{4}}x\)
1.8.6.21.
Answer.
\(x-{\frac{12}{13}}x\)
1.8.6.23.
Answer.
\(11x+2\)
1.8.6.25.
Answer.
\(x-20 = 50\)
1.8.6.27.
Answer.
\(\frac{x}{8} = 5\)
1.8.6.29.
Answer.
\(x-38 = 34\)
1.8.6.31.
Answer.
\(\frac{x}{14} = 13\)
1.8.6.33.
Answer.
\(14x-3 = 5\)
1.8.6.35.
Answer.
\(6\mathopen{}\left(x+9\right) = 12\)
1.8.6.37.
Answer.
\(9x = 2x-13\)

Applications

1.8.6.39.
Answer.
\(510t = 360\)
1.8.6.41.
Answer.
\(100+56t = 282\)
1.8.6.43.
Answer.
\(6+0.25t = 10\)
1.8.6.45.
Answer.
\(389.5+4.12t = 780\)
1.8.6.47.
Answer.
\(57+28t = 212\)
1.8.6.49.
Answer.
\(425-27t = 250\)
1.8.6.51.
Answer.
\(100-7t = 30\)
1.8.6.53.
Answer.
\(90+13n = 350\)
1.8.6.55.
Answer.
\(S+0.024S = 57999\)
1.8.6.57.
Answer.
\(p+0.067p = 472\)
1.8.6.59.
Answer.
\(p-0.2p = 332\)
1.8.6.61.
Answer.
\(b+0.18b = 73.2\)
1.8.6.63.
Answer.
\(r+0.025r = 1360\)
1.8.6.65.
Answer.
\(80+8.3454V\le 1900\)
1.8.6.67.
Answer.
\(7.8-0.5t\ge 0.5\)
1.8.6.69.
Answer.
\(S+0.029S < 71385\)
1.8.6.71.
Answer.
\(b+0.2b\le 79.65\)

Challenge

1.8.6.73.
Answer.
\(\$10.62\)

1.9 Variables, Expressions, and Equations Chapter Review

Review Exercises for Chapter 1

Section 1: Variables and Evaluating Expressions
1.9.1.
1.9.1.a
Answer 1.
\(t\hbox{, }T\hbox{, }x\hbox{, or }y\)
Answer 2.
\({\text{hours or minutes}}\)
1.9.1.b
Answer 1.
\(a\hbox{, }A\hbox{, }s\hbox{, }S\hbox{, }x\hbox{, or }y\)
Answer 2.
\({\verb!ft^2 or m^2!}\)
1.9.3.
Answer.
\(-13\)
1.9.5.
1.9.5.a
Answer.
\(512\)
1.9.5.b
Answer.
\(-216\)
1.9.7.
Answer.
\(-5\)
1.9.9.
Answer.
\(-1\)
1.9.11.
Answer.
\(291\ {\rm mi}\)
1.9.13.
Answer.
\(70\ {\rm feet}\)
1.9.15.
Answer.
\(5280x\)
1.9.17.
Answer.
\(140+40n\)
Section 2: Combining Like Terms
1.9.19.
Answer.
\(\frac{7}{3}e\)
1.9.21.
Answer.
\(\frac{-32}{7}q\)
1.9.23.
Answer.
\(\frac{29}{30}B+\frac{4}{3}A\)
1.9.25.
1.9.25.a
Answer.
\(24p+19c\)
1.9.25.b
Answer.
\(40p+39c\)
Section 3: Comparison Symbols and Notation for Intervals
1.9.27.
Answer.
\(\text{False}\)
1.9.29.
Answer.
\({\verb!<!}\)
1.9.31.
Answer.
\(9.5>4.2>3.6>-4>-4.1\)
1.9.33.
Answer 1.
\(\left\{x \mid x > 2\right\}\)
Answer 2.
\(\left(2,\infty \right)\)
1.9.35.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,5\right)\right\}\)
Answer 2.
\(\left\{x \mid x < 5\right\}\)
1.9.37.
Answer 1.
\(\left\{\mathrm{pH} \mid \mathrm{pH} < 7\right\}\)
Answer 2.
\(\left(-\infty ,7\right)\)
Section 4: Equations, Inequalities, and Solutions
1.9.39.
Answer 1.
\(-58\)
Answer 2.
\(-52\)
Answer 3.
\(\text{No, it is not a solution.}\)
1.9.41.
Answer 1.
\(48\)
Answer 2.
\(\text{No, it is not a solution.}\)
1.9.43.
Answer 1.
\({\frac{11}{2}}\)
Answer 2.
\({\frac{13}{2}}\)
Answer 3.
\(\text{No, it is not a solution.}\)
1.9.45.
Answer 1.
\(51\)
Answer 2.
\(\text{Yes, it is a solution.}\)
1.9.47.
Answer 1.
\(730\)
Answer 2.
\(\text{Yes, it is a solution.}\)
1.9.49.
Answer 1.
\(49.8087\)
Answer 2.
\(\text{No, it is not a solution.}\)
Section 5: Solving One-Step Equations
1.9.51.
Answer.
\(\left\{-12\right\}\)
1.9.53.
Answer.
\(\left\{10.3\right\}\)
1.9.55.
Answer 1.
\(6.25+N = 17.5\)
Answer 2.
\(11.25\ {\rm in}\)
Section 6: Solving One-Step Inequalities
1.9.57.
Answer 1.
\(\left\{\text{interval}, \left[4,\infty \right)\right\}\)
Answer 2.
\(\left[4,\infty \right)\)
Answer 3.
\(\left\{p \mid p\ge 4\right\}\)
Section 7: Algebraic Properties and Simplifying Expressions
1.9.59.
Answer.
\(0\)
1.9.61.
Answer.
\(\left(L+10\right)\cdot 4\)
1.9.63.
Answer.
\(\frac{-22}{21}x\)
1.9.65.
Answer.
\(-2i+21\)
Section 8: Modeling with Equations and Inequalities
1.9.67.
Answer.
\(5+x\)
1.9.69.
Answer.
\(x-{\frac{9}{14}}x\)
1.9.71.
Answer.
\(3x-13 = 12\)
1.9.73.
Answer.
\(12-0.05d = 1\)
1.9.75.
Answer.
\(425-24t = 275\)
1.9.77.
Answer.
\(S+0.028S = 66466\)
1.9.79.
Answer.
\(7.7-0.7t\ge 0.4\)

2 Linear Equations and Inequalities
2.1 Solving Multistep Linear Equations
2.1.6 Exercises

Review and Warmup

2.1.6.1.
Answer.
\(\left\{-6\right\}\)
2.1.6.3.
Answer.
\(\left\{-17\right\}\)
2.1.6.5.
Answer.
\(\left\{\frac{2}{7}\right\}\)

Vocabulary

2.1.6.7.
2.1.6.7.a
Answer.
\(\text{solve}\)
2.1.6.7.b
Answer.
\(\text{simplified}\)
2.1.6.7.c
Answer.
\(\text{simplify}\)
2.1.6.7.d
Answer.
\(\text{evaluate}\)

Skills Practice

2.1.6.9.
Answer.
\(\left\{6\right\}\)
2.1.6.11.
Answer.
\(\left\{-7\right\}\)
2.1.6.13.
Answer.
\(\left\{-1\right\}\)
2.1.6.15.
Answer.
\(\left\{\frac{13}{6}\right\}\)
2.1.6.17.
Answer.
\(\left\{\frac{-5}{9}\right\}\)
2.1.6.19.
Answer.
\(\left\{\frac{-1}{2}\right\}\)
2.1.6.21.
Answer.
\(\left\{0.756757\right\}\)
2.1.6.23.
Answer.
\(\left\{0.366197\right\}\)
2.1.6.25.
Answer.
\(\left\{-0.6\right\}\)
2.1.6.27.
Answer.
\(\left\{2\right\}\)
2.1.6.29.
Answer.
\(\left\{7\right\}\)
2.1.6.31.
Answer.
\(\left\{-6\right\}\)
2.1.6.33.
Answer.
\(\left\{4\right\}\)
2.1.6.35.
Answer.
\(\left\{6\right\}\)
2.1.6.37.
Answer.
\(\left\{-8\right\}\)
2.1.6.39.
Answer.
\(\left\{\frac{-1}{4}\right\}\)
2.1.6.41.
Answer.
\(\left\{\frac{-3}{2}\right\}\)
2.1.6.43.
Answer.
\(\left\{\frac{67}{25}\right\}\)
2.1.6.45.
Answer.
\(\left\{\frac{-26}{31}\right\}\)
2.1.6.47.
Answer.
\(\left\{2\right\}\)
2.1.6.49.
Answer.
\(\left\{8\right\}\)
2.1.6.51.
Answer.
\(\left\{\frac{7}{4}\right\}\)

Applications

2.1.6.53.
Answer.
\(4.25862\ {\rm hr}\)
2.1.6.55.
Answer.
\(12\ {\rm yr}\)
2.1.6.57.
Answer.
\(58.913\ {\rm weeks}\)
2.1.6.59.
Answer.
\(6.16\ {\rm min}\)
2.1.6.61.
Answer.
\(7.14286\ {\rm min}\)
2.1.6.63.
Answer.
\(8.88889\ {\rm days}\)
2.1.6.65.
Answer.
\(23\)
2.1.6.67.
Answer.
\(\$60{,}685.36\)
2.1.6.69.
Answer.
\(\$462.11\)
2.1.6.71.
Answer.
\(\$1{,}251.23\)

2.2 Solving Multistep Linear Inequalities
2.2.4 Exercises

Review and Warmup

2.2.4.1.
Answer 1.
\(\left\{\text{interval}, \left(-3,\infty \right)\right\}\)
Answer 2.
\(\left(-3,\infty \right)\)
Answer 3.
\(\left\{D \mid D > -3\right\}\)
2.2.4.3.
Answer 1.
\(\left\{\text{interval}, \left[8,\infty \right)\right\}\)
Answer 2.
\(\left[8,\infty \right)\)
Answer 3.
\(\left\{P \mid P\ge 8\right\}\)

Skills Practice

2.2.4.5.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,5\right]\right\}\)
Answer 2.
\(\left(-\infty ,5\right]\)
Answer 3.
\(\left\{b \mid b\le 5\right\}\)
2.2.4.7.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-4\right]\right\}\)
Answer 2.
\(\left(-\infty ,-4\right]\)
Answer 3.
\(\left\{m \mid m\le -4\right\}\)
2.2.4.9.
Answer 1.
\(\left\{\text{interval}, \left[-1,\infty \right)\right\}\)
Answer 2.
\(\left[-1,\infty \right)\)
Answer 3.
\(\left\{y \mid y\ge -1\right\}\)
2.2.4.11.
Answer 1.
\(\left\{\text{interval}, \left[3,\infty \right)\right\}\)
Answer 2.
\(\left[3,\infty \right)\)
Answer 3.
\(\left\{J \mid J\ge 3\right\}\)
2.2.4.13.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-6\right]\right\}\)
Answer 2.
\(\left(-\infty ,-6\right]\)
Answer 3.
\(\left\{V \mid V\le -6\right\}\)
2.2.4.15.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-2\right)\right\}\)
Answer 2.
\(\left(-\infty ,-2\right)\)
Answer 3.
\(\left\{g \mid g < -2\right\}\)
2.2.4.17.
Answer 1.
\(\left\{\text{interval}, \left[2,\infty \right)\right\}\)
Answer 2.
\(\left[2,\infty \right)\)
Answer 3.
\(\left\{s \mid s\ge 2\right\}\)
2.2.4.19.
Answer 1.
\(\left\{\text{interval}, \left[6,\infty \right)\right\}\)
Answer 2.
\(\left[6,\infty \right)\)
Answer 3.
\(\left\{D \mid D\ge 6\right\}\)
2.2.4.21.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-3\right)\right\}\)
Answer 2.
\(\left(-\infty ,-3\right)\)
Answer 3.
\(\left\{P \mid P < -3\right\}\)
2.2.4.23.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,1\right]\right\}\)
Answer 2.
\(\left(-\infty ,1\right]\)
Answer 3.
\(\left\{b \mid b\le 1\right\}\)
2.2.4.25.
Answer 1.
\(\left\{\text{interval}, \left[5,\infty \right)\right\}\)
Answer 2.
\(\left[5,\infty \right)\)
Answer 3.
\(\left\{l \mid l\ge 5\right\}\)
2.2.4.27.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-4\right]\right\}\)
Answer 2.
\(\left(-\infty ,-4\right]\)
Answer 3.
\(\left\{x \mid x\le -4\right\}\)
2.2.4.29.
Answer 1.
\(\left\{\text{interval}, \left(-1,\infty \right)\right\}\)
Answer 2.
\(\left(-1,\infty \right)\)
Answer 3.
\(\left\{I \mid I > -1\right\}\)
2.2.4.31.
Answer 1.
\(\left\{\text{interval}, \left(4,\infty \right)\right\}\)
Answer 2.
\(\left(4,\infty \right)\)
Answer 3.
\(\left\{V \mid V > 4\right\}\)

Applications

2.2.4.33.
2.2.4.33.a
Answer.
\(15+2x\le 43\)
2.2.4.33.b
Answer.
\(14\ {\rm mi}\)
2.2.4.33.c
Answer.
\(\left[0,14\right]\)
2.2.4.35.
2.2.4.35.a
Answer.
\(47+24x\ge 212\)
2.2.4.35.b
Answer.
\(6.875\ {\rm min}\)
2.2.4.35.c
Answer.
\(\left[6.875,\infty \right)\)
2.2.4.37.
2.2.4.37.a
Answer.
\(x+0.08x < 94485\)
2.2.4.37.b
Answer.
\(87486\)
2.2.4.37.c
Answer.
\(\left[10000,87486\right)\)

2.3 Equations and Inequalities with Fractions
2.3.5 Exercises

Review and Warmup

2.3.5.1.
Answer.
\(44\)
2.3.5.3.
Answer.
\(630\)
2.3.5.5.
Answer.
\(210\)

Skills Practice

2.3.5.7.
Answer 1.
\(3\)
Answer 2.
\(\left\{\frac{1}{3}\right\}\)
2.3.5.9.
Answer 1.
\(12\)
Answer 2.
\(\left\{\frac{-125}{36}\right\}\)
2.3.5.11.
Answer 1.
\(5\)
Answer 2.
\(\left\{17\right\}\)
2.3.5.13.
Answer 1.
\(35\)
Answer 2.
\(\left\{\frac{-295}{28}\right\}\)
2.3.5.15.
Answer 1.
\(100\)
Answer 2.
\(\left\{\frac{-765}{4}\right\}\)
2.3.5.17.
Answer 1.
\(30\)
Answer 2.
\(\left\{2\right\}\)
2.3.5.19.
Answer 1.
\(4\)
Answer 2.
\(\left\{\frac{29}{15}\right\}\)
2.3.5.21.
Answer 1.
\(21\)
Answer 2.
\(\left\{\frac{-224}{165}\right\}\)
2.3.5.23.
Answer 1.
\(105\)
Answer 2.
\(\left\{\frac{-831}{395}\right\}\)
2.3.5.25.
Answer 1.
\(60\)
Answer 2.
\(\left\{\frac{325}{23}\right\}\)
2.3.5.27.
Answer 1.
\(11\)
Answer 2.
\(\left\{x \mid x\le \frac{29}{11}\right\}\)
Answer 3.
\(\left(-\infty ,{\frac{29}{11}}\right]\)
2.3.5.29.
Answer 1.
\(5\)
Answer 2.
\(\left\{x \mid x\ge \frac{-52}{11}\right\}\)
Answer 3.
\(\left[-{\frac{52}{11}},\infty \right)\)
2.3.5.31.
Answer 1.
\(60\)
Answer 2.
\(\left\{x \mid x > \frac{-284}{35}\right\}\)
Answer 3.
\(\left(-{\frac{284}{35}},\infty \right)\)
2.3.5.33.
Answer 1.
\(10\)
Answer 2.
\(\left\{x \mid x > \frac{1}{15}\right\}\)
Answer 3.
\(\left({\frac{1}{15}},\infty \right)\)
2.3.5.35.
Answer 1.
\(36\)
Answer 2.
\(\left\{x \mid x\ge \frac{57}{194}\right\}\)
Answer 3.
\(\left[{\frac{57}{194}},\infty \right)\)

Applications

2.3.5.37.
Answer.
\(15.2903\ {\rm s}\)
2.3.5.39.
Answer.
\(12\ {\rm yr}\)
2.3.5.41.
Answer.
\(82.5\)
2.3.5.43.
Answer.
\(50\ {\rm g}\)
2.3.5.45.
Answer.
\(\$86.13\)
2.3.5.47.
Answer.
\(129\)

Challenge

2.3.5.49.
Answer.
\(24\)

2.4 Special Solution Sets
2.4.4 Exercises

Notation

2.4.4.1.
Answer.
\(\text{no real solutions}\)

Skills Practice

2.4.4.3.
Answer.
\(\text{no real solutions}\)
2.4.4.5.
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
2.4.4.7.
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
2.4.4.9.
Answer.
\(\text{no real solutions}\)
2.4.4.11.
Answer.
\(\text{no real solutions}\)
2.4.4.13.
Answer.
\(\text{no real solutions}\)
2.4.4.15.
Answer.
\(\text{no real solutions}\)
2.4.4.17.
Answer.
\(\text{no real solutions}\)
2.4.4.19.
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
2.4.4.21.
Answer.
\(\text{no real solutions}\)
2.4.4.23.
Answer.
\(\text{no real solutions}\)
2.4.4.25.
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
2.4.4.27.
Answer.
\(\text{no real solutions}\)
2.4.4.29.
Answer.
\(\text{no real solutions}\)
2.4.4.31.
Answer.
\(\text{no real solutions}\)
2.4.4.33.
Answer.
\(\text{no real solutions}\)
2.4.4.35.
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
2.4.4.37.
Answer.
\(\text{no real solutions}\)
2.4.4.39.
Answer.
\(\text{no real solutions}\)

Challenge

2.4.4.41.
Answer 1.
\(9x+42\)
Answer 2.
\(10\mathopen{}\left(x+4\right)\)

2.5 Isolating a Linear Variable
2.5.3 Exercises

Skills Practice

2.5.3.1.
2.5.3.1.a
Answer.
\(\left\{1\right\}\)
2.5.3.1.b
Answer.
\(G = x-X\)
2.5.3.3.
2.5.3.3.a
Answer.
\(\left\{12\right\}\)
2.5.3.3.b
Answer.
\(S = q+m\)
2.5.3.5.
2.5.3.5.a
Answer.
\(\left\{\frac{9}{7}\right\}\)
2.5.3.5.b
Answer.
\(e = \frac{h}{D}\)
2.5.3.7.
2.5.3.7.a
Answer.
\(\left\{24\right\}\)
2.5.3.7.b
Answer.
\(q = YS\)
2.5.3.9.
2.5.3.9.a
Answer.
\(\left\{\frac{1}{2}\right\}\)
2.5.3.9.b
Answer.
\(B = \frac{D-Q}{i}\)
2.5.3.11.
Answer.
\(L = G-y\)
2.5.3.13.
Answer.
\(Y = \frac{w-x}{M}\)
2.5.3.15.
Answer.
\(x = \frac{y-q}{e}\)
2.5.3.17.
Answer.
\(u = s\mathopen{}\left(r-g\right)\)

Applications

2.5.3.19.
Answer.
\(b = \frac{2A}{h}\)
2.5.3.21.
Answer.
\(m = \frac{y-b}{x}\)
2.5.3.23.
Answer.
\(r = \frac{c}{2\pi }\)
2.5.3.25.
Answer.
\(h = \frac{V}{\pi r^{2}}\)
2.5.3.27.
Answer.
\(y = 4x+4\)
2.5.3.29.
Answer.
\(y = -{\frac{3}{7}}x+3\)
2.5.3.31.
Answer.
\(y = x+{\frac{2}{9}}\)
2.5.3.33.
Answer.
\(y = -{\frac{7}{3}}x+{\frac{17}{33}}\)

2.6 Linear Equations and Inequalities Chapter Review

Review Exercises for Chapter 2

Section 1: Solving Multistep Linear Equations
2.6.1.
2.6.1.a
Answer.
\(\text{simplified}\)
2.6.1.b
Answer.
\(\text{evaluate}\)
2.6.1.c
Answer.
\(\text{solve}\)
2.6.1.d
Answer.
\(\text{simplify}\)
2.6.3.
Answer.
\(\left\{-0.0697674\right\}\)
2.6.5.
Answer.
\(\left\{1\right\}\)
2.6.7.
Answer.
\(\left\{\frac{-6}{7}\right\}\)
2.6.9.
Answer.
\({\frac{72}{11}}\ {\rm yr}\)
2.6.11.
Answer.
\(2.81818\ {\rm hr}\)
2.6.13.
Answer.
\(\$458.17\)
Section 2: Solving Multistep Linear Inequalities
2.6.15.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-6\right)\right\}\)
Answer 2.
\(\left(-\infty ,-6\right)\)
Answer 3.
\(\left\{F \mid F < -6\right\}\)
2.6.17.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-2\right]\right\}\)
Answer 2.
\(\left(-\infty ,-2\right]\)
Answer 3.
\(\left\{R \mid R\le -2\right\}\)
2.6.19.
Answer 1.
\(\left\{\text{interval}, \left[2,\infty \right)\right\}\)
Answer 2.
\(\left[2,\infty \right)\)
Answer 3.
\(\left\{d \mid d\ge 2\right\}\)
2.6.21.
2.6.21.a
Answer.
\(15+4x\le 95\)
2.6.21.b
Answer.
\(20\ {\rm mi}\)
2.6.21.c
Answer.
\(\left[0,20\right]\)
Section 3: Equations and Inequalities with Fractions
2.6.23.
Answer 1.
\(7\)
Answer 2.
\(\left\{\frac{-27}{49}\right\}\)
2.6.25.
Answer 1.
\(210\)
Answer 2.
\(\left\{1\right\}\)
2.6.27.
Answer 1.
\(7\)
Answer 2.
\(\left\{x \mid x\ge \frac{-61}{84}\right\}\)
Answer 3.
\(\left[-{\frac{61}{84}},\infty \right)\)
2.6.29.
Answer 1.
\(3\)
Answer 2.
\(\left\{x \mid x > 3\right\}\)
Answer 3.
\(\left(3,\infty \right)\)
2.6.31.
Answer.
\({\frac{72}{5}}\ {\rm yr}\)
2.6.33.
Answer.
\(\$94.62\)
Section 4: Special Solution Sets
2.6.35.
Answer.
\(\text{no real solutions}\)
2.6.37.
Answer.
\(\text{no real solutions}\)
2.6.39.
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
2.6.41.
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
Section 5: Isolating a Linear Variable
2.6.43.
Answer.
\(x = \frac{y-u}{p}\)
2.6.45.
Answer.
\(m = \frac{y-b}{x}\)
2.6.47.
Answer.
\(y = 8x-1\)

3 Graphing Lines
3.1 Cartesian Coordinates

Exercises

3.1.1.
Answer 1.
\(\left(1,2\right)\)
Answer 2.
\(\left(-1,-2\right)\)
Answer 3.
\(\left(0,4\right)\)
Answer 4.
\(\left(-3,0\right)\)
3.1.3.
Answer.
\(\left\{\text{point}, \left(0,-1\right)\right\}, \left\{\text{point}, \left(5,-3\right)\right\}, \left\{\text{point}, \left(1,-8\right)\right\}, \left\{\text{point}, \left(4,0\right)\right\}\)
3.1.5.
Answer.
\(\left\{\text{point}, \left(-5,0.666667\right)\right\}, \left\{\text{point}, \left(-3.66667,-2\right)\right\}\)
3.1.7.
Answer.
\(\left\{\text{point}, \left(-2.75,-4.25\right)\right\}, \left\{\text{point}, \left(0.75,2.25\right)\right\}\)
3.1.9.
Answer.
\(\left\{\text{point}, \left(149,108\right)\right\}, \left\{\text{point}, \left(176,115\right)\right\}\)
3.1.11.
Answer.
\(\left\{\text{fill}, \left(1,1\right)\right\}, \left\{\text{fill}, \left(-1,1\right)\right\}\)
3.1.13.
Answer.
\(\left\{\text{fill}, \left(1,1\right)\right\}, \left\{\text{fill}, \left(-1,-1\right)\right\}\)
3.1.15.
Answer 1.
\(\left(20,1\right)\)
Answer 2.
\(\left(20,1\right)\)
3.1.17.
Answer 1.
\(\text{III}\)
Answer 2.
\(\text{IV}\)
Answer 3.
\(\text{I}\)
Answer 4.
\(\text{IV}\)
3.1.19.
Answer 1.
\(\text{III}\)
Answer 2.
\(\text{IV}\)
Answer 3.
\(\text{I}\)
Answer 4.
\(\text{IV}\)

3.2 Graphing Equations

Exercises

Skills Practice
3.2.1.
Answer.
\(\text{Choice 1, Choice 3}\)
3.2.3.
Answer.
\(\text{Choice 3, Choice 4}\)
3.2.5.
Answer.
\(\text{Choice 1, Choice 3}\)
3.2.7.
Answer.
\(\text{Choice 1, Choice 2}\)
3.2.9.
Answer 1.
\(1;\,\left(-2,1\right);\,-1;\,\left(-1,-1\right);\,-3;\,\left(0,-3\right);\,-5;\,\left(1,-5\right);\,-7;\,\left(2,-7\right)\)
Answer 2.
\(\left\{\text{point}, \left(-2,1\right)\right\}, \left\{\text{point}, \left(-1,-1\right)\right\}, \left\{\text{point}, \left(0,-3\right)\right\}, \left\{\text{point}, \left(1,-5\right)\right\}, \left\{\text{point}, \left(2,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-2,1\right), \left(-1,-1\right)\right\}\)
3.2.11.
Answer 1.
\(7;\,\left(-6,7\right);\,3;\,\left(-3,3\right);\,-1;\,\left(0,-1\right);\,-5;\,\left(3,-5\right);\,-9;\,\left(6,-9\right)\)
Answer 2.
\(\left\{\text{point}, \left(-6,7\right)\right\}, \left\{\text{point}, \left(-3,3\right)\right\}, \left\{\text{point}, \left(0,-1\right)\right\}, \left\{\text{point}, \left(3,-5\right)\right\}, \left\{\text{point}, \left(6,-9\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,7\right), \left(-3,3\right)\right\}\)
3.2.13.
Answer 1.
\(1;\,\left(-2,1\right);\,-4;\,\left(-1,-4\right);\,-7;\,\left(0,-7\right);\,-8;\,\left(1,-8\right);\,-7;\,\left(2,-7\right)\)
Answer 2.
\(\left\{\text{point}, \left(-2,1\right)\right\}, \left\{\text{point}, \left(-1,-4\right)\right\}, \left\{\text{point}, \left(0,-7\right)\right\}, \left\{\text{point}, \left(1,-8\right)\right\}, \left\{\text{point}, \left(2,-7\right)\right\}, \left\{\text{quadratic}, \text{solid}, \left(-2,1\right), \left(-1,-4\right), \left(0,-7\right)\right\}\)
3.2.15.
Answer 1.
\(-2;\,\left(-2,-2\right);\,1;\,\left(-1,1\right);\,0;\,\left(0,0\right);\,1;\,\left(1,1\right);\,10;\,\left(2,10\right)\)
Answer 2.
\(\left\{\text{point}, \left(-2,-2\right)\right\}, \left\{\text{point}, \left(-1,1\right)\right\}, \left\{\text{point}, \left(0,0\right)\right\}, \left\{\text{point}, \left(1,1\right)\right\}, \left\{\text{point}, \left(2,10\right)\right\}, \left\{\text{cubic}, \text{solid}, \left(-2,-2\right), \left(-1,1\right), \left(0,0\right), \left(1,1\right)\right\}\)
3.2.17.
Answer.
\(\text{Choice 1, Choice 2, Choice 4}\)
Applications
3.2.19.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,900\right), \left(1,925\right)\right\}\)
3.2.21.
Answer.
\(\left\{\text{line}, \text{solid}, \left(40,100\right), \left(90,110\right)\right\}\)

3.3 Exploring Two-Variable Data and Rate of Change
3.3.5 Exercises

Skills Practice

3.3.5.1.
Answer.
\(y = 4x\)
3.3.5.3.
Answer.
\(y = x+4\)
3.3.5.5.
Answer.
\(y = x-3\)
3.3.5.7.
Answer.
\(y = \sqrt{x}\)
3.3.5.9.
Answer.
\(y = x^{2}\)
3.3.5.11.
Answer.
\(y = \frac{1}{x}\)
3.3.5.13.
Answer.
\({\frac{9}{13}}\)
3.3.5.15.
Answer.
\(9.125\)
3.3.5.17.
Answer.
\({\frac{153}{28}}\)
3.3.5.19.
Answer.
\(-1\)
3.3.5.21.
Answer.
\(-{\frac{5}{3}}\)
3.3.5.23.
Answer.
\({\frac{16}{35}}\)
3.3.5.25.
Answer.
\({\frac{4}{3}}\)
3.3.5.27.
Answer.
\({\frac{767}{40}}\)
3.3.5.29.
Answer.
\(\text{yes}\)
3.3.5.31.
Answer.
\(\text{yes}\)
3.3.5.33.
Answer.
\(\text{no}\)
3.3.5.35.
Answer.
\(\text{no}\)
3.3.5.37.
Answer.
\(\text{yes}\)
3.3.5.39.
Answer.
\(\text{yes}\)

Applications

3.3.5.41.
3.3.5.41.a
Answer.
\(2840.57\ {\textstyle\frac{\rm\mathstrut people}{\rm\mathstrut yr}}\)
3.3.5.41.b
Answer.
\(-6608\ {\textstyle\frac{\rm\mathstrut people}{\rm\mathstrut yr}}\)
3.3.5.41.c
Answer.
\(\left[2003,2004\right], \left[2019\right], \left[2020,2021\right], \left[2021,2022\right]\)
3.3.5.41.d
Answer.
\(\left[2006,2016\right]\)
3.3.5.41.e
Answer.
\(10203.9\ {\textstyle\frac{\rm\mathstrut people}{\rm\mathstrut yr}}\)

3.4 Slope
3.4.5 Exercises

Skills Practice

3.4.5.1.
Answer.
\(7\)
3.4.5.3.
Answer.
\(-1\)
3.4.5.5.
Answer.
\({\frac{1}{3}}\)
3.4.5.7.
Answer.
\(-{\frac{1}{4}}\)
3.4.5.9.
Answer.
\({\frac{9}{4}}\)
3.4.5.11.
Answer.
\(-3.24\)
3.4.5.13.
Answer.
\(0\)
3.4.5.15.
Answer.
\({\frac{501}{670}}\)
3.4.5.17.
Answer.
\(-{\frac{245}{8}}\)
3.4.5.19.
Answer.
\(7\)
3.4.5.21.
Answer.
\(3\)
3.4.5.23.
Answer.
\({\frac{3}{10}}\)
3.4.5.25.
Answer.
\(0\)
3.4.5.27.
Answer.
\(1\)
3.4.5.29.
Answer.
\(1.12046\)
3.4.5.31.
Answer.
\({\frac{12}{5}}\)
3.4.5.33.
Answer.
\({\frac{17}{11}}\)
3.4.5.35.
Answer.
\(1.91935\)
3.4.5.37.
Answer.
\(\left\{\text{line}, \text{solid}, \left(-3,-1\right), \left(0,3\right)\right\}\)
3.4.5.39.
Answer.
\(\left\{\text{line}, \text{solid}, \left(1,-2\right), \left(4,-4\right)\right\}\)
3.4.5.41.
Answer.
\(\left\{\text{line}, \text{solid}, \left(-8,-8\right), \left(-5,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-8\right), \left(-4,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-8\right), \left(-3,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,-8\right), \left(-2,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,-8\right), \left(-1,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-3,-8\right), \left(0,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-2,-8\right), \left(1,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-1,-8\right), \left(2,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,-8\right), \left(3,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(1,-8\right), \left(4,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(2,-8\right), \left(5,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(3,-8\right), \left(6,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(4,-8\right), \left(7,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(5,-8\right), \left(8,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-7\right), \left(-5,-6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-6\right), \left(-5,-5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-5\right), \left(-5,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-4\right), \left(-5,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-3\right), \left(-5,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-2\right), \left(-5,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-1\right), \left(-5,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,0\right), \left(-5,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,1\right), \left(-5,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,2\right), \left(-5,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,3\right), \left(-5,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,4\right), \left(-5,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,5\right), \left(-5,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,6\right), \left(-5,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,7\right), \left(-5,8\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-7\right), \left(-4,-6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-6\right), \left(-4,-5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-5\right), \left(-4,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-4\right), \left(-4,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-3\right), \left(-4,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-2\right), \left(-4,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-1\right), \left(-4,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,0\right), \left(-4,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,1\right), \left(-4,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,2\right), \left(-4,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,3\right), \left(-4,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,4\right), \left(-4,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,5\right), \left(-4,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,6\right), \left(-4,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,7\right), \left(-4,8\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-7\right), \left(-3,-6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-6\right), \left(-3,-5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-5\right), \left(-3,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-4\right), \left(-3,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-3\right), \left(-3,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-2\right), \left(-3,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-1\right), \left(-3,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,0\right), \left(-3,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,1\right), \left(-3,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,2\right), \left(-3,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,3\right), \left(-3,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,4\right), \left(-3,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,5\right), \left(-3,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,6\right), \left(-3,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,7\right), \left(-3,8\right)\right\}\)
3.4.5.43.
Answer.
\(\left\{\text{line}, \text{solid}, \left(-8,-13\right), \left(-6,-18\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-12\right), \left(-6,-17\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-11\right), \left(-6,-16\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-10\right), \left(-6,-15\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-9\right), \left(-6,-14\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-8\right), \left(-6,-13\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-7\right), \left(-6,-12\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-6\right), \left(-6,-11\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-5\right), \left(-6,-10\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-4\right), \left(-6,-9\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-3\right), \left(-6,-8\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-2\right), \left(-6,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-1\right), \left(-6,-6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,0\right), \left(-6,-5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,1\right), \left(-6,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,2\right), \left(-6,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,3\right), \left(-6,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,4\right), \left(-6,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,5\right), \left(-6,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,6\right), \left(-6,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,7\right), \left(-6,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,8\right), \left(-6,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,9\right), \left(-6,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,10\right), \left(-6,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,11\right), \left(-6,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,12\right), \left(-6,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,13\right), \left(-6,8\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-13\right), \left(-5,-18\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-12\right), \left(-5,-17\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-11\right), \left(-5,-16\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-10\right), \left(-5,-15\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-9\right), \left(-5,-14\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-8\right), \left(-5,-13\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-7\right), \left(-5,-12\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-6\right), \left(-5,-11\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-5\right), \left(-5,-10\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-4\right), \left(-5,-9\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-3\right), \left(-5,-8\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-2\right), \left(-5,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-1\right), \left(-5,-6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,0\right), \left(-5,-5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,1\right), \left(-5,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,2\right), \left(-5,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,3\right), \left(-5,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,4\right), \left(-5,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,5\right), \left(-5,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,6\right), \left(-5,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,7\right), \left(-5,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,8\right), \left(-5,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,9\right), \left(-5,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,10\right), \left(-5,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,11\right), \left(-5,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,12\right), \left(-5,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,13\right), \left(-5,8\right)\right\}\)

Applications

3.4.5.45.
Answer 1.
\(375\ {\textstyle\frac{\rm\mathstrut ft}{\rm\mathstrut h}}\)
Answer 2.
\(125\ {\textstyle\frac{\rm\mathstrut ft}{\rm\mathstrut h}}\)
Answer 3.
\(0\ {\textstyle\frac{\rm\mathstrut ft}{\rm\mathstrut h}}\)
Answer 4.
\(-500\ {\textstyle\frac{\rm\mathstrut ft}{\rm\mathstrut h}}\)
3.4.5.47.
Answer.
\(-8\ {\textstyle\frac{\rm\mathstrut ml}{\rm\mathstrut min}}\)

Challenge

3.4.5.49.
Answer.
\(\text{True}\)

3.5 Slope-Intercept Form
3.5.7 Exercises

Skills Practice

3.5.7.1.
Answer 1.
\(2\)
Answer 2.
\(\left(0,7\right)\)
3.5.7.3.
Answer 1.
\(-7\)
Answer 2.
\(\left(0,-2\right)\)
3.5.7.5.
Answer 1.
\(1\)
Answer 2.
\(\left(0,1\right)\)
3.5.7.7.
Answer 1.
\(-1\)
Answer 2.
\(\left(0,5\right)\)
3.5.7.9.
Answer 1.
\({\frac{8}{5}}\)
Answer 2.
\(\left(0,9\right)\)
3.5.7.11.
Answer 1.
\(-6.2\)
Answer 2.
\(\left(0,-6\right)\)
3.5.7.13.
Answer 1.
\(5\)
Answer 2.
\(\left(0,6\right)\)
3.5.7.15.
Answer 1.
\(-7\)
Answer 2.
\(\left(0,8\right)\)
3.5.7.17.
Answer.
\(y = 2x+3\)
3.5.7.19.
Answer.
\(y = {\frac{1}{4}}x-4\)
3.5.7.21.
Answer.
\(y = x-2\)
3.5.7.23.
Answer.
\(y = x+4\)
3.5.7.25.
Answer.
\(y = {\frac{1}{3}}x+2\)
3.5.7.27.
Answer.
\(y = {\frac{5}{4}}x\)
3.5.7.29.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,5\right), \left(1,7\right)\right\}\)
3.5.7.31.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,2\right), \left(1,-1\right)\right\}\)
3.5.7.33.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-3\right), \left(-4,-2\right)\right\}\)
3.5.7.35.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-4\right), \left(5,-3\right)\right\}\)
3.5.7.37.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,0\right), \left(9,2\right)\right\}\)
3.5.7.39.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-1\right), \left(7,3\right)\right\}\)
3.5.7.41.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,1\right), \left(1,2\right)\right\}\)
3.5.7.43.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,5\right), \left(1,4\right)\right\}\)
3.5.7.45.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-2\right), \left(7,-11\right)\right\}\)
3.5.7.47.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,2\right), \left(10,-4\right)\right\}\)
3.5.7.49.
Answer.
\(y = 9x-2\)
3.5.7.51.
Answer.
\(y = -3x+3\)
3.5.7.53.
Answer.
\(y = 6x+7\)
3.5.7.55.
Answer.
\(y = {\frac{8}{7}}x-8\)
3.5.7.57.
Answer.
\(y = -{\frac{3}{4}}x-4\)
3.5.7.59.
Answer.
\(y = {\frac{14}{19}}x+62\)
3.5.7.61.
Answer.
\(y = 4.5x+4.4\)

Applications

3.5.7.63.
Answer.
\(14\)
3.5.7.65.
Answer.
\(360\)
3.5.7.67.
Answer.
\(45\)
3.5.7.69.
Answer 1.
\(y = 0.06x+19\)
Answer 2.
\(\$29.20\)
Answer 3.
\(490\)
3.5.7.71.
Answer 1.
\(y = 0.27x+13.2\)
Answer 2.
\(21.03\)
Answer 3.
\(59\)
3.5.7.73.
Answer 1.
\(y = -22000x+831000\)
Answer 2.
\(\$611{,}000\)
Answer 3.
\(2037\)
3.5.7.75.
Answer 1.
\(y = -8.9x+382.7\)
Answer 2.
\(62.3\)
Answer 3.
\(43\)

3.6 Point-Slope Form
3.6.5 Exercises

Skills Practice

3.6.5.1.
Answer 1.
\(2\)
Answer 2.
\(\left(6,5\right)\)
3.6.5.3.
Answer 1.
\(-4\)
Answer 2.
\(\left(-8,3\right)\)
3.6.5.5.
Answer 1.
\(6\)
Answer 2.
\(\left(-2,-3\right)\)
3.6.5.7.
Answer 1.
\(7\)
Answer 2.
\(\left(4,-9\right)\)
3.6.5.9.
Answer.
\(y = 9\mathopen{}\left(x-6\right)+7\)
3.6.5.11.
Answer.
\(y = 3\mathopen{}\left(x+9\right)-6\)
3.6.5.13.
Answer.
\(y = -1.7\mathopen{}\left(x-5\right)-8\)
3.6.5.15.
Answer.
\(y = 6\mathopen{}\left(x-7\right)+3\hbox{ or }y = 6\mathopen{}\left(x-4\right)-15\)
3.6.5.17.
Answer.
\(y = -7\mathopen{}\left(x-8\right)-9\hbox{ or }y = -7\mathopen{}\left(x-4\right)+19\)
3.6.5.19.
Answer.
\(y = \frac{-3}{7}\mathopen{}\left(x+8\right)-5\hbox{ or }y = \frac{-3}{7}\mathopen{}\left(x+57\right)+16\)
3.6.5.21.
Answer.
\(y = \frac{7}{5}\mathopen{}\left(x+4\right)+1\hbox{ or }y = \frac{7}{5}\mathopen{}\left(x-6\right)+15\)
3.6.5.23.
Answer.
\(y = 6x-43\)
3.6.5.25.
Answer.
\(y = -7x-9\)
3.6.5.27.
Answer.
\(y = \frac{2}{7}x+\frac{10}{7}\)
3.6.5.29.
Answer.
\(y = -5.7x+\left(-37.81\right)\)
3.6.5.31.
Answer.
\(y = \frac{8}{7}\mathopen{}\left(x+4\right)-2\hbox{ or }y = \frac{8}{7}\mathopen{}\left(x-3\right)+6\)
3.6.5.33.
Answer.
\(y = \frac{-5}{8}\mathopen{}\left(x+2\right)+3\hbox{ or }y = \frac{-5}{8}\mathopen{}\left(x-6\right)-2\)
3.6.5.35.
Answer.
\(y = 20\mathopen{}\left(x-2\right)+300\hbox{ or }y = 20\mathopen{}\left(x-7\right)+400\)
3.6.5.37.
Answer.
\(y = \frac{-57}{4}\mathopen{}\left(x-1\right)+297\hbox{ or }y = \frac{-57}{4}\mathopen{}\left(x-9\right)+183\)
3.6.5.39.
Answer.
\(\left\{\text{line}, \text{solid}, \left(3,2\right), \left(4,6\right)\right\}\)
3.6.5.41.
Answer.
\(\left\{\text{line}, \text{solid}, \left(3,-4\right), \left(4,-2\right)\right\}\)
3.6.5.43.
Answer.
\(\left\{\text{line}, \text{solid}, \left(-8,-9\right), \left(-3,-2\right)\right\}\)
3.6.5.45.
Answer.
\(\left\{\text{line}, \text{solid}, \left(-3,8\right), \left(2,6\right)\right\}\)
3.6.5.47.
Answer.
\(\left\{\text{line}, \text{solid}, \left(3,4\right), \left(13,12\right)\right\}\)

Applications

3.6.5.49.
Answer 1.
\(y = 0.04\mathopen{}\left(x-240\right)+26.6\)
Answer 2.
\(\$25.00\)
Answer 3.
\(430\)
3.6.5.51.
Answer 1.
\(y = 0.22\mathopen{}\left(x-11\right)+13.92\)
Answer 2.
\(18.1\)
Answer 3.
\(52\)
3.6.5.53.
Answer 1.
\(y = -45000\mathopen{}\left(x-2\right)+658000\hbox{ or }y = -45000\mathopen{}\left(x-7\right)+433000\)
Answer 2.
\(\$253{,}000\)
Answer 3.
\(2016\)
3.6.5.55.
Answer 1.
\(y = -7.1\mathopen{}\left(x-10\right)+213\hbox{ or }y = -7.1\mathopen{}\left(x-12\right)+198.8\)
Answer 2.
\(7.1\)
Answer 3.
\(40\)

3.7 Standard Form
3.7.5 Exercises

Review and Warmup

3.7.5.1.
Answer.
\(y = -9x+11\)
3.7.5.3.
Answer.
\(y = -x+9\)
3.7.5.5.
Answer.
\(y = -{\frac{66}{23}}x+{\frac{206}{23}}\)

Skills Practice

3.7.5.7.
Answer 1.
\(\left(4,0\right)\)
Answer 2.
\(\left(0,8\right)\)
Answer 3.
\(-{\frac{1}{2}}\)
3.7.5.9.
Answer 1.
\(\left(5,0\right)\)
Answer 2.
\(\left(0,-3\right)\)
Answer 3.
\({\frac{5}{3}}\)
3.7.5.11.
Answer 1.
\(\left({\frac{5}{7}},0\right)\)
Answer 2.
\(\left(0,{\frac{5}{6}}\right)\)
Answer 3.
\(-{\frac{6}{7}}\)
3.7.5.13.
Answer 1.
\(\left({\frac{49}{47}},0\right)\)
Answer 2.
\(\left(0,-{\frac{49}{40}}\right)\)
Answer 3.
\({\frac{40}{47}}\)
3.7.5.15.
Answer 1.
\(\left(24,0\right)\)
Answer 2.
\(\left(0,{\frac{40}{3}}\right)\)
Answer 3.
\(-{\frac{9}{5}}\)
3.7.5.17.
Answer 1.
\(\left(-1.27273,0\right)\)
Answer 2.
\(\left(0,0.875\right)\)
Answer 3.
\(1.45455\)
3.7.5.19.
Answer.
\(6x-y=-3\)
3.7.5.21.
Answer.
\(8x-9y=27\)
3.7.5.23.
Answer.
\(\left\{\text{line}, \text{solid}, \left(2,0\right), \left(0,5\right)\right\}, \left\{\text{point}, \left(2,0\right)\right\}, \left\{\text{point}, \left(0,5\right)\right\}\)
3.7.5.25.
Answer.
\(\left\{\text{line}, \text{solid}, \left(-4,0\right), \left(0,7\right)\right\}, \left\{\text{point}, \left(-4,0\right)\right\}, \left\{\text{point}, \left(0,7\right)\right\}\)
3.7.5.27.
Answer.
\(\left\{\text{line}, \text{solid}, \left(-5,0\right), \left(0,-9\right)\right\}, \left\{\text{point}, \left(-5,0\right)\right\}, \left\{\text{point}, \left(0,-9\right)\right\}\)

Applications

3.7.5.29.
Answer.
\(0.6x+0.15y=99.6\)
3.7.5.31.
Answer.
\(4.93x+2.25y=4.66\)

Challenge

3.7.5.33.
3.7.5.33.a
Answer 1.
\(13\)
Answer 2.
\(2\)
Answer 3.
\(3\)
3.7.5.33.b
Answer 1.
\(2\)
Answer 2.
\(13\)
Answer 3.
\(3\)

3.8 Geometry of Lines
3.8.5 Exercises

Review and Warmup

3.8.5.1.
Answer.
\(y = 8\mathopen{}\left(x-7\right)+6\hbox{ or }y = 8\mathopen{}\left(x-3\right)-26\)
3.8.5.3.
Answer.
\(y = \frac{-5}{7}\mathopen{}\left(x+9\right)-8\hbox{ or }y = \frac{-5}{7}\mathopen{}\left(x-19\right)-28\)
3.8.5.5.
Answer.
\(\text{Choice 1, Choice 4}\)
3.8.5.7.
Answer.
\(\text{Choice 2, Choice 4}\)

Skills Practice

3.8.5.9.
Answer 1.
\(4;\,-2;\,\left(4,-2\right);\,4;\,-1;\,\left(4,-1\right);\,4;\,0;\,\left(4,0\right);\,4;\,1;\,\left(4,1\right);\,4;\,2;\,\left(4,2\right)\)
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(4,-2\right), \left(4,-1\right)\right\}\)
3.8.5.11.
Answer 1.
\(-2;\,8;\,\left(-2,8\right);\,-1;\,8;\,\left(-1,8\right);\,0;\,8;\,\left(0,8\right);\,1;\,8;\,\left(1,8\right);\,2;\,8;\,\left(2,8\right)\)
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(-2,8\right), \left(-1,8\right)\right\}\)
3.8.5.13.
Answer.
\(y = -5\)
3.8.5.15.
Answer.
\(x = -2\)
3.8.5.17.
Answer.
\(x = 2\)
3.8.5.19.
Answer.
\(y = 6\)
3.8.5.21.
Answer 1.
\(\text{NONE}\)
Answer 2.
\(\left(0,-9\right)\)
3.8.5.23.
Answer 1.
\(\left(-5,0\right)\)
Answer 2.
\(\text{NONE}\)
3.8.5.25.
Answer.
\(\text{distinct and parallel}\)
3.8.5.27.
Answer.
\(\text{perpendicular}\)
3.8.5.29.
Answer.
\(\text{none of the above}\)
3.8.5.31.
Answer.
\(\text{same line}\)
3.8.5.33.
Answer 1.
\(y-0.75x = -6.25\)
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(7,-1\right), \left(-5,-10\right)\right\}\)
3.8.5.35.
Answer 1.
\(0.444444x+y = 1.66667\)
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(6,-1\right), \left(24,-9\right)\right\}\)
3.8.5.37.
Answer 1.
\(x = 7\)
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(7,8\right), \left(7,4\right)\right\}\)
3.8.5.39.
Answer 1.
\(y = -8\)
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(4,-8\right), \left(5,-8\right)\right\}\)

3.9 Strategies for Graphing Lines
3.9.5 Exercises

3.9.5.1.

Answer 1.
\(3;\,\left(-2,3\right);\,2;\,\left(-1,2\right);\,1;\,\left(0,1\right);\,0;\,\left(1,0\right);\,-1;\,\left(2,-1\right)\)
Answer 2.
\(\left\{\text{point}, \left(-2,3\right)\right\}, \left\{\text{point}, \left(-1,2\right)\right\}, \left\{\text{point}, \left(0,1\right)\right\}, \left\{\text{point}, \left(1,0\right)\right\}, \left\{\text{point}, \left(2,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-2,3\right), \left(-1,2\right)\right\}\)

3.9.5.3.

Answer 1.
\(8;\,\left(-8,8\right);\,5;\,\left(-4,5\right);\,2;\,\left(0,2\right);\,-1;\,\left(4,-1\right);\,-4;\,\left(8,-4\right)\)
Answer 2.
\(\left\{\text{point}, \left(-8,8\right)\right\}, \left\{\text{point}, \left(-4,5\right)\right\}, \left\{\text{point}, \left(0,2\right)\right\}, \left\{\text{point}, \left(4,-1\right)\right\}, \left\{\text{point}, \left(8,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,8\right), \left(-4,5\right)\right\}\)

3.9.5.5.

Answer 1.
\(6;\,-2;\,\left(6,-2\right);\,6;\,-1;\,\left(6,-1\right);\,6;\,0;\,\left(6,0\right);\,6;\,1;\,\left(6,1\right);\,6;\,2;\,\left(6,2\right)\)
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(6,-2\right), \left(6,-1\right)\right\}\)

3.9.5.7.

Answer 1.
\(-2;\,-9;\,\left(-2,-9\right);\,-1;\,-9;\,\left(-1,-9\right);\,0;\,-9;\,\left(0,-9\right);\,1;\,-9;\,\left(1,-9\right);\,2;\,-9;\,\left(2,-9\right)\)
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(-2,-9\right), \left(-1,-9\right)\right\}\)

3.9.5.9.

Answer.
\(\left\{\text{line}, \text{solid}, \left(3,0\right), \left(0,7\right)\right\}, \left\{\text{point}, \left(3,0\right)\right\}, \left\{\text{point}, \left(0,7\right)\right\}\)

3.9.5.11.

Answer.
\(\left\{\text{line}, \text{solid}, \left(5,0\right), \left(0,-9\right)\right\}, \left\{\text{point}, \left(5,0\right)\right\}, \left\{\text{point}, \left(0,-9\right)\right\}\)

3.9.5.13.

Answer.
\(\left\{\text{line}, \text{solid}, \left(-7,0\right), \left(0,-4\right)\right\}, \left\{\text{point}, \left(-7,0\right)\right\}, \left\{\text{point}, \left(0,-4\right)\right\}\)

3.9.5.15.

Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-3\right), \left(1,2\right)\right\}\)

3.9.5.17.

Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-5\right), \left(1,-7\right)\right\}\)

3.9.5.19.

Answer.
\(\left\{\text{line}, \text{solid}, \left(0,2\right), \left(-3,3\right)\right\}\)

3.9.5.21.

Answer.
\(\left\{\text{line}, \text{solid}, \left(0,3\right), \left(4,4\right)\right\}\)

3.9.5.23.

Answer.
\(\left\{\text{line}, \text{solid}, \left(0,4\right), \left(3,12\right)\right\}\)

3.9.5.25.

Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-9\right), \left(1,-8\right)\right\}\)

3.9.5.27.

Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-1\right), \left(8,-4\right)\right\}\)

3.9.5.29.

Answer.
\(\left\{\text{line}, \text{solid}, \left(3,5\right), \left(4,9\right)\right\}\)

3.9.5.31.

Answer.
\(\left\{\text{line}, \text{solid}, \left(4,-2\right), \left(5,1\right)\right\}\)

3.9.5.33.

Answer.
\(\left\{\text{line}, \text{solid}, \left(-8,-3\right), \left(-3,0\right)\right\}\)

3.9.5.35.

Answer.
\(\left\{\text{line}, \text{solid}, \left(-8,4\right), \left(-5,-4\right)\right\}\)

3.9.5.37.

Answer.
\(\left\{\text{line}, \text{solid}, \left(-9,8\right), \left(1,5\right)\right\}\)

3.9.5.39.

Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-2\right), \left(1,2\right)\right\}\)

3.9.5.41.

Answer.
\(\left\{\text{line}, \text{solid}, \left(0,1\right), \left(3,-7\right)\right\}\)

3.9.5.43.

Answer.
\(\left\{\text{line}, \text{solid}, \left(-8,-2\right), \left(-5,0\right)\right\}\)

3.9.5.45.

Answer.
\(\left\{\text{line}, \text{solid}, \left(3,0\right), \left(0,4\right)\right\}, \left\{\text{point}, \left(3,0\right)\right\}, \left\{\text{point}, \left(0,4\right)\right\}\)

3.9.5.47.

Answer.
\(\left\{\text{line}, \text{solid}, \left(-1,-2\right), \left(-1,-1\right)\right\}\)

3.9.5.49.

Answer.
\(\left\{\text{line}, \text{solid}, \left(-2,3\right), \left(-1,3\right)\right\}\)

3.10 Graphing Lines Chapter Review

Review Exercises for Chapter 3

Section 1: Cartesian Coordinates
3.10.1.
Answer 1.
\(\left(1,0\right)\)
Answer 2.
\(\left(3,-1\right)\)
Answer 3.
\(\left(0,-2\right)\)
Answer 4.
\(\left(-3,-4\right)\)
3.10.3.
Answer.
\(\left\{\text{point}, \left(0,3\right)\right\}, \left\{\text{point}, \left(-8,0\right)\right\}, \left\{\text{point}, \left(2,-6\right)\right\}, \left\{\text{point}, \left(6,-1\right)\right\}\)
3.10.5.
Answer.
\(\left\{\text{fill}, \left(1,1\right)\right\}, \left\{\text{fill}, \left(1,-1\right)\right\}\)
3.10.7.
Answer 1.
\(\text{III}\)
Answer 2.
\(\text{IV}\)
Answer 3.
\(\text{IV}\)
Answer 4.
\(\text{I}\)
Section 2: Graphing Equations
3.10.9.
Answer.
\(\text{Choice 1, Choice 2}\)
3.10.11.
Answer 1.
\(-13;\,\left(-2,-13\right);\,-2;\,\left(-1,-2\right);\,1;\,\left(0,1\right);\,2;\,\left(1,2\right);\,7;\,\left(2,7\right)\)
Answer 2.
\(\left\{\text{point}, \left(-2,-13\right)\right\}, \left\{\text{point}, \left(-1,-2\right)\right\}, \left\{\text{point}, \left(0,1\right)\right\}, \left\{\text{point}, \left(1,2\right)\right\}, \left\{\text{point}, \left(2,7\right)\right\}, \left\{\text{cubic}, \text{solid}, \left(-2,-13\right), \left(-1,-2\right), \left(0,1\right), \left(1,2\right)\right\}\)
Section 3: Exploring Two-Variable Data and Rate of Change
3.10.13.
Answer.
\(y = 6x\)
3.10.15.
Answer.
\(y = x^{2}\)
3.10.17.
Answer.
\(-{\frac{9}{50}}\)
3.10.19.
Answer.
\({\frac{3}{2}}\)
3.10.21.
Answer.
\(\text{yes}\)
Section 4: Slope
3.10.23.
Answer.
\({\frac{8}{9}}\)
3.10.25.
Answer.
\({\frac{400}{231}}\)
3.10.27.
Answer.
\(0.872449\)
3.10.29.
Answer.
\(\left\{\text{line}, \text{solid}, \left(-8,-8\right), \left(-5,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-7\right), \left(-5,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-6\right), \left(-5,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-5\right), \left(-5,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-8\right), \left(-4,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-7\right), \left(-4,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-6\right), \left(-4,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-5\right), \left(-4,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-8\right), \left(-3,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-7\right), \left(-3,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-6\right), \left(-3,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-5\right), \left(-3,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,-8\right), \left(-2,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,-7\right), \left(-2,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,-6\right), \left(-2,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,-5\right), \left(-2,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,-8\right), \left(-1,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,-7\right), \left(-1,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,-6\right), \left(-1,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,-5\right), \left(-1,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-3,-8\right), \left(0,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-3,-7\right), \left(0,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-3,-6\right), \left(0,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-3,-5\right), \left(0,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-2,-8\right), \left(1,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-2,-7\right), \left(1,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-2,-6\right), \left(1,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-2,-5\right), \left(1,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-1,-8\right), \left(2,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-1,-7\right), \left(2,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-1,-6\right), \left(2,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-1,-5\right), \left(2,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,-8\right), \left(3,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,-7\right), \left(3,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,-6\right), \left(3,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,-5\right), \left(3,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(1,-8\right), \left(4,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(1,-7\right), \left(4,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(1,-6\right), \left(4,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(1,-5\right), \left(4,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(2,-8\right), \left(5,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(2,-7\right), \left(5,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(2,-6\right), \left(5,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(2,-5\right), \left(5,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(3,-8\right), \left(6,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(3,-7\right), \left(6,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(3,-6\right), \left(6,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(3,-5\right), \left(6,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(4,-8\right), \left(7,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(4,-7\right), \left(7,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(4,-6\right), \left(7,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(4,-5\right), \left(7,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(5,-8\right), \left(8,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(5,-7\right), \left(8,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(5,-6\right), \left(8,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(5,-5\right), \left(8,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-4\right), \left(-5,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-3\right), \left(-5,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-2\right), \left(-5,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-1\right), \left(-5,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,0\right), \left(-5,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,1\right), \left(-5,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,2\right), \left(-5,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,3\right), \left(-5,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,4\right), \left(-5,8\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-4\right), \left(-4,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-3\right), \left(-4,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-2\right), \left(-4,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-1\right), \left(-4,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,0\right), \left(-4,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,1\right), \left(-4,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,2\right), \left(-4,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,3\right), \left(-4,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,4\right), \left(-4,8\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-4\right), \left(-3,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-3\right), \left(-3,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-2\right), \left(-3,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-1\right), \left(-3,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,0\right), \left(-3,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,1\right), \left(-3,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,2\right), \left(-3,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,3\right), \left(-3,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,4\right), \left(-3,8\right)\right\}\)
3.10.31.
Answer.
\(-6.66667\ {\textstyle\frac{\rm\mathstrut ml}{\rm\mathstrut min}}\)
Section 5: Slope-Intercept Form
3.10.33.
Answer 1.
\({\frac{6}{5}}\)
Answer 2.
\(\left(0,-8\right)\)
3.10.35.
Answer.
\(y = x-2\)
3.10.37.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-2\right), \left(-4,-1\right)\right\}\)
3.10.39.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,1\right), \left(9,-6\right)\right\}\)
3.10.41.
Answer.
\(y = -{\frac{8}{7}}x+9\)
3.10.43.
Answer.
\(15\)
3.10.45.
Answer 1.
\(y = -5x+220\)
Answer 2.
\(60\)
Answer 3.
\(44\)
Section 6: Point-Slope Form
3.10.47.
Answer 1.
\(7\)
Answer 2.
\(\left(8,9\right)\)
3.10.49.
Answer.
\(y = 8\mathopen{}\left(x-2\right)+7\)
3.10.51.
Answer.
\(y = 2\mathopen{}\left(x-5\right)+7\hbox{ or }y = 2\mathopen{}\left(x-6\right)+9\)
3.10.53.
Answer.
\(y = -4x-23\)
3.10.55.
Answer.
\(y = \frac{-5}{3}\mathopen{}\left(x+1\right)+7\hbox{, }y = \frac{-5}{3}\mathopen{}\left(x-2\right)+2\hbox{, or }y = \frac{-5}{3}\mathopen{}\left(x-5\right)-3\)
3.10.57.
Answer.
\(\left\{\text{line}, \text{solid}, \left(4,2\right), \left(5,5\right)\right\}\)
3.10.59.
Answer 1.
\(y = -49000\mathopen{}\left(x-4\right)+636000\)
Answer 2.
\(\$391{,}000\)
Answer 3.
\(2016\)
3.10.61.
Answer 1.
\(y = 0.13\mathopen{}\left(x-14\right)+19.92\hbox{ or }y = 0.13\mathopen{}\left(x-19\right)+20.57\)
Answer 2.
\(22\)
Answer 3.
\(56\)
Section 7: Standard Form
3.10.63.
Answer 1.
\(\left(2.28571,0\right)\)
Answer 2.
\(\left(0,-1.54839\right)\)
Answer 3.
\(1.47619\)
3.10.65.
Answer.
\(7x+5y=-5\)
3.10.67.
Answer.
\(\left\{\text{line}, \text{solid}, \left(-8,0\right), \left(0,-7\right)\right\}, \left\{\text{point}, \left(-8,0\right)\right\}, \left\{\text{point}, \left(0,-7\right)\right\}\)
Section 8: Geometry of Lines
3.10.69.
Answer 1.
\(-2;\,-8;\,\left(-2,-8\right);\,-1;\,-8;\,\left(-1,-8\right);\,0;\,-8;\,\left(0,-8\right);\,1;\,-8;\,\left(1,-8\right);\,2;\,-8;\,\left(2,-8\right)\)
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(-2,-8\right), \left(-1,-8\right)\right\}\)
3.10.71.
Answer 1.
\(\text{NONE}\)
Answer 2.
\(\left(0,-4\right)\)
3.10.73.
Answer.
\(\text{none of the above}\)

4 Systems of Two Linear Equations
4.1 Solving a System by Graphing
4.1.5 Exercises

Review

4.1.5.1.
Answer.
\(\text{Choice 2, Choice 4, Choice 6}\)

Skills Practice

4.1.5.3.
Answer.
\(\text{Yes, it is a solution.}\)
4.1.5.5.
Answer.
\(\text{No, it is not a solution.}\)
4.1.5.7.
Answer.
\(\text{No, it is not a solution.}\)
4.1.5.9.
Answer.
\(\left(-2,4\right)\)
4.1.5.11.
Answer.
\(\left(1,-4\right)\)
4.1.5.13.
Answer.
\(\text{no solutions}\)
4.1.5.15.
Answer 1.
\(\text{One}\)
Answer 2.
\(\text{None of the above}\)
4.1.5.17.
Answer 1.
\(\text{Infinitely many}\)
Answer 2.
\(\text{Dependent}\)
4.1.5.19.
Answer 1.
\(\text{Zero}\)
Answer 2.
\(\text{Inconsistent}\)
4.1.5.21.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(0,7\right), \left(4,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,-3\right), \left(4,2\right)\right\}\)
Answer 2.
\(\left(4,2\right)\)
4.1.5.23.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(3,-2\right), \left(8,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(6,9\right), \left(8,6\right)\right\}\)
Answer 2.
\(\left(8,6\right)\)
4.1.5.25.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(-1,-4\right), \left(2,-9\right)\right\}, \left\{\text{line}, \text{solid}, \left(6,7\right), \left(9,2\right)\right\}\)
Answer 2.
\(\text{no solutions}\)
4.1.5.27.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(-2,0\right), \left(0,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,0\right), \left(0,-2\right)\right\}\)
Answer 2.
\(\left(-4,-1\right)\)
4.1.5.29.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(2,0\right), \left(0,4\right)\right\}, \left\{\text{line}, \text{solid}, -16, \left(0,-6\right)\right\}\)
Answer 2.
\(\text{no solutions}\)
4.1.5.31.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(4,0\right), \left(0,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(4,-1\right), \left(0,-5\right)\right\}\)
Answer 2.
\(\text{no solutions}\)
4.1.5.33.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(-5,0\right), \left(0,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-4\right), \left(5,2\right)\right\}\)
Answer 2.
\(\left(5,2\right)\)
4.1.5.35.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(3,0\right), \left(0,-1\right)\right\}\)
Answer 2.
\(\text{infinitely many solutions}\)
4.1.5.37.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(0,1\right), \left(1,9\right)\right\}, \left\{\text{line}, \text{solid}, \left(9,-4\right), \left(19,-1\right)\right\}\)
Answer 2.
\(\text{infinitely many solutions}\)
4.1.5.39.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(0,-2\right), \left(4,-3\right)\right\}\)
Answer 2.
\(\left(4,-3\right)\)

Applications

4.1.5.41.
4.1.5.41.a
Answer 1.
\(3x+2y = 54\)
Answer 2.
\(x+y = 24\)
4.1.5.41.b
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,27\right), \left(18,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,24\right), \left(24,0\right)\right\}\)
4.1.5.41.c
Answer 1.
\(6\)
Answer 2.
\(18\)
4.1.5.43.
4.1.5.43.a
Answer 1.
\(d = 3t\)
Answer 2.
\(d = 110+\left(-8\right)t\)
4.1.5.43.b
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,0\right), \left(1,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,110\right), \left(1,102\right)\right\}\)
4.1.5.43.c
Answer 1.
\(10\ {\rm s}\)
Answer 2.
\(30\ {\rm m}\)

4.2 Substitution
4.2.5 Exercises

Skills Practice

4.2.5.1.
Answer.
\(E = 4, D = -5\)
4.2.5.3.
Answer.
\(Q = 1, V = 3\)
4.2.5.5.
Answer.
\(c = -2, k = -6\)
4.2.5.7.
Answer.
\(n = -4, A = 2\)
4.2.5.9.
Answer.
\(z = -7, P = 7\)
4.2.5.11.
Answer.
\(\text{no solutions}\)
4.2.5.13.
Answer.
\(\text{infinitely many solutions}\)
4.2.5.15.
Answer.
\(h = 1, K = -3\)
4.2.5.17.
Answer.
\(\text{no solutions}\)
4.2.5.19.
Answer.
\(E = -4, r = -5\)
4.2.5.21.
Answer.
\(Q = -{\frac{11}{4}}, F = -{\frac{87}{4}}\)
4.2.5.23.
Answer.
\(\text{infinitely many solutions}\)
4.2.5.25.
Answer.
\(m = {\frac{13}{5}}, l = {\frac{51}{5}}\)
4.2.5.27.
Answer.
\(y = {\frac{64}{5}}, C = {\frac{83}{5}}\)
4.2.5.29.
Answer.
\(J = -{\frac{19}{9}}, S = -{\frac{34}{9}}\)
4.2.5.31.
Answer.
\(W = -{\frac{12}{5}}, h = -8\)
4.2.5.33.
Answer.
\(h = 1, y = 4\)
4.2.5.35.
Answer.
\(t = -1.11765, N = -4.44118\)
4.2.5.37.
Answer.
\(E = -0.250609, d = -1.18558\)
4.2.5.39.
Answer.
\(P = {\frac{26}{15}}, t = {\frac{19}{9}}\)
4.2.5.41.
Answer.
\(b = 15, I = {\frac{27}{5}}\)
4.2.5.43.
Answer.
\(m = -{\frac{1}{2}}, Z = -{\frac{3}{10}}\)
4.2.5.45.
Answer.
\(\text{no solutions}\)
4.2.5.47.
Answer.
\(J = {\frac{135}{4}}, D = -{\frac{15}{2}}\)
4.2.5.49.
Answer 1.
\(W = -36, T = {\frac{122}{3}}\)
Answer 2.
\(16\)
4.2.5.51.
Answer.
\(\text{infinitely many solutions}\)

Applications

4.2.5.53.
Answer 1.
\(L = 4W-8\)
Answer 2.
\(2L+2W = 139\)
Answer 3.
\(54\ {\rm ft}\)
Answer 4.
\(15.5\ {\rm ft}\)
4.2.5.55.
Answer 1.
\(B = 36.95+4.25D\)
Answer 2.
\(B = 45.95+3.2D\)
Answer 3.
\(8.57143\ {\rm GB}\)
Answer 4.
\(\$73.38\)
4.2.5.57.
Answer 1.
\(M+S = 29\)
Answer 2.
\(2M+8S = 100\)
Answer 3.
\(22\)
Answer 4.
\(7\)
4.2.5.59.
Answer 1.
\(x+y = 3900\)
Answer 2.
\(0.015x-0.07y = -212.5\)
Answer 3.
\(\$1{,}100\)
Answer 4.
\(\$2{,}800\)
4.2.5.61.
Answer 1.
\(x+y = 555\)
Answer 2.
\(0.1x+0.18y = 69.93\)
Answer 3.
\(375\ {\rm ml}\)
Answer 4.
\(180\ {\rm ml}\)

4.3 Elimination
4.3.5 Exercises

Skills Practice

4.3.5.1.
Answer.
\(I = -2, r = 1\)
4.3.5.3.
Answer.
\(V = -4, G = 6\)
4.3.5.5.
Answer.
\(g = -7, X = -2\)
4.3.5.7.
Answer.
\(s = 6, m = 4\)
4.3.5.9.
Answer.
\(\text{no solutions}\)
4.3.5.11.
Answer.
\(P = 1, S = 4\)
4.3.5.13.
Answer.
\(b = {\frac{7}{3}}, j = 1\)
4.3.5.15.
Answer.
\(l = -{\frac{32}{3}}, y = {\frac{34}{3}}\)
4.3.5.17.
Answer.
\(x = 17.6111, N = -2.27778\)
4.3.5.19.
Answer.
\(I = {\frac{17}{12}}, e = {\frac{9}{8}}\)
4.3.5.21.
Answer.
\(\text{infinitely many solutions}\)
4.3.5.23.
Answer.
\(\text{no solutions}\)
4.3.5.25.
Answer.
\(s = -2, Z = 5\)
4.3.5.27.
Answer.
\(C = -4, p = -3\)
4.3.5.29.
Answer.
\(N = -7, E = 4\)
4.3.5.31.
Answer.
\(\text{infinitely many solutions}\)

Applications

4.3.5.33.
Answer 1.
\(M+S = 36\)
Answer 2.
\(2M+6S = 100\)
Answer 3.
\(29\)
Answer 4.
\(7\)
4.3.5.35.
Answer 1.
\(x+y = 4700\)
Answer 2.
\(0.02x+0.055y = 223.5\)
Answer 3.
\(\$1{,}000\)
Answer 4.
\(\$3{,}700\)

Challenge

4.3.5.37.
Answer.
\(3\)

4.4 Systems of Two Linear Equations Chapter Review

Review Exercises for Chapter 4

Section 1: Solving a System by Graphing
4.4.1.
Answer.
\(\text{Yes, it is a solution.}\)
4.4.3.
Answer.
\(\text{no solutions}\)
4.4.5.
Answer 1.
\(\text{Infinitely many}\)
Answer 2.
\(\text{Dependent}\)
4.4.7.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(-1,0\right), \left(0,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,1\right), \left(-4,9\right)\right\}\)
Answer 2.
\(\left(-4,9\right)\)
4.4.9.
4.4.9.a
Answer 1.
\(d = 3t\)
Answer 2.
\(d = 150+\left(-12\right)t\)
4.4.9.b
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,0\right), \left(1,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,150\right), \left(1,138\right)\right\}\)
4.4.9.c
Answer 1.
\(10\ {\rm s}\)
Answer 2.
\(30\ {\rm m}\)
Section 2: Substitution
4.4.11.
Answer.
\(T = 4, R = 7\)
4.4.13.
Answer.
\(\text{infinitely many solutions}\)
4.4.15.
Answer.
\(r = 0.0714286, z = -0.2\)
4.4.17.
Answer.
\(C = -2, N = {\frac{29}{14}}\)
4.4.19.
Answer 1.
\(R = 96000-4500t\)
Answer 2.
\(R = 41000+2000t\)
Answer 3.
\(8.46154\ {\rm months}\)
Answer 4.
\(\$0\)
4.4.21.
Answer 1.
\(P+C = 1\)
Answer 2.
\(1.6P+5.76C = 3\)
Answer 3.
\(0.663462\ {\rm lb}\)
Answer 4.
\(0.336538\ {\rm lb}\)
Section 3: Elimination
4.4.23.
Answer.
\(k = 4, J = 2\)
4.4.25.
Answer.
\(\text{no solutions}\)
4.4.27.
Answer 1.
\(x+y = 4200\)
Answer 2.
\(0.015x+0.05y = 157.5\)
Answer 3.
\(\$1{,}500\)
Answer 4.
\(\$2{,}700\)
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