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Appendix D 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
Answer 1.
\(d\hbox{, }D\hbox{, }x\hbox{, or }y\)
Answer 2.
Answer 1.
\(w\hbox{, }W\hbox{, }x\hbox{, or }y\)
Answer 2.
Answer.
\(-2{\textstyle\frac{1}{2}}\)
Applications
Answer.
\(5.62912\ {\rm seconds}\)
1.2 Combining Like Terms
1.2.5 Exercises
Prerequisite/Review Skills
Skills Practice
Answer.
\(-{\frac{7}{10}}e, {\frac{3}{8}}C, -g, 7.3c\)
Answer.
\({\frac{3}{10}}z^{2}, -13, 49z\)
Answer.
\(-\frac{2}{3}t+\frac{9}{4}B\)
Answer.
\(\frac{11}{18}R^{3}+\frac{3}{2}R^{5}\)
Answer.
\(-\frac{35}{18}K-\frac{26}{9}s\)
Answer.
\(\frac{3}{10}t^{2}+t^{6}\)
Applications
Answer.
\(\frac{22}{15}F+\frac{11}{5}C\)
Answer.
\(\frac{13}{7}c+\frac{31}{6}j+\frac{10}{3}m\)
1.3 Comparison Symbols and Notation for Intervals
1.3.4 Exercises
Prerequisite/Review Skills
Skills Practice
Answer.
\(9.2>7.3>-2.3>-3.1>-3.6\)
Answer.
\({\frac{15}{8}}>{\frac{16}{9}}>{\frac{7}{6}}>{\frac{1}{2}}>{\frac{1}{3}}\)
Answer.
\(8>{\frac{2}{3}}>{\frac{9}{16}}>\sqrt{2}>\frac{\pi }{4}\)
Answer 1.
\(\left\{x \mid x < -7\right\}\)
Answer 2.
\(\left(-\infty ,-7\right)\)
Answer 1.
\(\left\{x \mid x\le -4\right\}\)
Answer 2.
\(\left(-\infty ,-4\right]\)
Answer 1.
\(\left\{x \mid x\ge -1\right\}\)
Answer 2.
\(\left[-1,\infty \right)\)
Answer 1.
\(\left\{x \mid x > 3\right\}\)
Answer 2.
\(\left(3,\infty \right)\)
Answer 1.
\(\left\{\text{interval}, \left[6,\infty \right)\right\}\)
Answer 2.
\(\left[6,\infty \right)\)
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-6\right)\right\}\)
Answer 2.
\(\left(-\infty ,-6\right)\)
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-2\right]\right\}\)
Answer 2.
\(\left(-\infty ,-2\right]\)
Answer 1.
\(\left\{\text{interval}, \left(1,\infty \right)\right\}\)
Answer 2.
\(\left(1,\infty \right)\)
Answer 1.
\(\left\{\text{interval}, \left[4,\infty \right)\right\}\)
Answer 2.
\(\left\{x \mid x\ge 4\right\}\)
Answer 1.
\(\left\{\text{interval}, \left(-7,\infty \right)\right\}\)
Answer 2.
\(\left\{x \mid x > -7\right\}\)
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-4\right)\right\}\)
Answer 2.
\(\left\{x \mid x < -4\right\}\)
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-1\right]\right\}\)
Answer 2.
\(\left\{x \mid x\le -1\right\}\)
Applications
Answer 1.
\(\left\{a \mid a\ge 21\right\}\)
Answer 2.
\(\left[21,\infty \right)\)
Answer 1.
\(\left\{d \mid d\ge 5000\right\}\)
Answer 2.
\(\left[5000,\infty \right)\)
Answer 1.
\(\left\{\mathrm{pH} \mid \mathrm{pH} < 7\right\}\)
Answer 2.
\(\left(-\infty ,7\right)\)
Challenge
1.4 Equations, Inequalities, and Solutions
1.4.6 Exercises
Prerequisite/Review Skills
Skills Practice
Answer 1.
Answer 2.
\(\text{No, it is not a solution.}\)
Answer 1.
Answer 2.
\(\text{No, it is not a solution.}\)
Answer 1.
Answer 2.
\(\text{No, it is not a solution.}\)
Answer 1.
Answer 2.
Answer 3.
\(\text{No, it is not a solution.}\)
Answer 1.
Answer 2.
Answer 3.
\(\text{No, it is not a solution.}\)
Answer 1.
Answer 2.
\(\text{No, it is not a solution.}\)
Answer 1.
Answer 2.
Answer 3.
\(\text{Yes, it is a solution.}\)
Answer 1.
Answer 2.
\(\text{No, it is not a solution.}\)
Answer 1.
Answer 2.
Answer 3.
\(\text{Yes, it is a solution.}\)
Answer 1.
Answer 2.
Answer 3.
\(\text{No, it is not a solution.}\)
Answer 1.
Answer 2.
\(\text{Yes, it is a solution.}\)
Answer 1.
Answer 2.
Answer 3.
\(\text{Yes, it is a solution.}\)
Answer 1.
Answer 2.
Answer 3.
\(\text{Yes, it is a solution.}\)
Answer 1.
Answer 2.
\(\text{No, it is not a solution.}\)
Answer 1.
Answer 2.
\(\text{Yes, it is a solution.}\)
Answer 1.
Answer 2.
\(\text{No, it is not a solution.}\)
Answer 1.
Answer 2.
Answer 3.
\(\text{Yes, it is a solution.}\)
Answer 1.
Answer 2.
Answer 3.
\(\text{Yes, it is a solution.}\)
Answer 1.
Answer 2.
\(\text{Yes, it is a solution.}\)
Answer 1.
Answer 2.
Answer 3.
\(\text{Yes, it is a solution.}\)
Answer 1.
Answer 2.
\(\text{No, it is not a solution.}\)
Answer 1.
Answer 2.
Answer 3.
\(\text{Yes, it is a solution.}\)
Answer 1.
Answer 2.
Answer 3.
\(\text{Yes, it is a solution.}\)
Answer 1.
Answer 2.
\(\text{Yes, it is a solution.}\)
Answer 1.
Answer 2.
Answer 3.
\(\text{No, it is not a solution.}\)
Answer 1.
Answer 2.
Answer 3.
\(\text{Yes, it is a solution.}\)
Answer.
\(\text{Choice 1, Choice 4, Choice 5}\)
Answer.
\(\text{Choice 3, Choice 6}\)
Answer.
\(\text{Choice 1, Choice 3, Choice 6}\)
Applications
Answer 1.
Answer 2.
\(\text{Yes, it is a solution.}\)
Answer 1.
Answer 2.
\(\text{Yes, it is a solution.}\)
Answer 1.
Answer 2.
\(\text{No, it is not a solution.}\)
Answer 1.
Answer 2.
Answer 3.
\(\text{Yes, it is a solution.}\)
Answer 1.
Answer 2.
\(\text{Yes, it is a solution.}\)
1.5 Solving One-Step Equations
1.5.6 Exercises
Review and Warmup
Skills Practice
Answer.
\(\left\{\frac{-4}{19}\right\}\)
Answer.
\(\left\{\frac{-63}{20}\right\}\)
Answer.
\(\left\{\frac{31}{12}\right\}\)
Answer.
\(\left\{\frac{11}{28}\right\}\)
Answer.
\(\left\{\frac{15}{16}\right\}\)
Answer.
\(\left\{\frac{1}{7}\right\}\)
Answer.
\(\left\{\frac{-1}{4}\right\}\)
Answer.
\(\left\{-18.16\right\}\)
Answer.
\(\left\{-29.44\right\}\)
Answer.
\(\left\{-0.240741\right\}\)
Applications
Answer 1.
Answer 2.
\(73.9234\ {\textstyle\frac{\rm\mathstrut ft}{\rm\mathstrut s}}\)
Challenge
1.6 Solving One-Step Inequalities
1.6.4 Exercises
Skills Practice
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-6\right)\right\}\)
Answer 2.
\(\left(-\infty ,-6\right)\)
Answer 3.
\(\left\{i \mid i < -6\right\}\)
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-2\right]\right\}\)
Answer 2.
\(\left(-\infty ,-2\right]\)
Answer 3.
\(\left\{t \mid t\le -2\right\}\)
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,2\right)\right\}\)
Answer 2.
\(\left(-\infty ,2\right)\)
Answer 3.
\(\left\{F \mid F < 2\right\}\)
Answer 1.
\(\left\{\text{interval}, \left(5,\infty \right)\right\}\)
Answer 2.
\(\left(5,\infty \right)\)
Answer 3.
\(\left\{Q \mid Q > 5\right\}\)
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,6\right)\right\}\)
Answer 2.
\(\left(-\infty ,6\right)\)
Answer 3.
\(\left\{c \mid c < 6\right\}\)
Answer 1.
\(\left\{\text{interval}, \left(-8,\infty \right)\right\}\)
Answer 2.
\(\left(-8,\infty \right)\)
Answer 3.
\(\left\{n \mid n > -8\right\}\)
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,4\right]\right\}\)
Answer 2.
\(\left(-\infty ,4\right]\)
Answer 3.
\(\left\{y \mid y\le 4\right\}\)
Answer 1.
\(\left\{\text{interval}, \left(5,\infty \right)\right\}\)
Answer 2.
\(\left(5,\infty \right)\)
Answer 3.
\(\left\{K \mid K > -\left(-5\right)\right\}\)
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-2\right]\right\}\)
Answer 2.
\(\left(-\infty ,-2\right]\)
Answer 3.
\(\left\{X \mid X\le -2\right\}\)
Answer 1.
\(\left\{\text{interval}, \left(3,\infty \right)\right\}\)
Answer 2.
\(\left(3,\infty \right)\)
Answer 3.
\(\left\{h \mid h > 3\right\}\)
1.7 Algebraic Properties and Simplifying Expressions
1.7.6 Exercises
Vocabulary
Skills Practice
Answer.
\(\left(t+{\frac{8}{7}}\right)+t^{2}\)
Answer.
\(2\mathopen{}\left(De\right)\)
Answer.
\(\left(y+5\right)\cdot 4\)
Answer.
\(7\mathopen{}\left(3+J\right)\)
Answer.
\(\frac{7}{2}s+\frac{7}{2}\frac{8}{3}\)
Answer.
\(-D-\left(\frac{9}{5}\right)\)
Answer.
\(\frac{93}{5}K+\frac{-139}{40}\)
Answer.
\(12.24l+\left(-3.06\right)\)
Critical Thinking
1.8 Modeling with Equations and Inequalities
1.8.6 Exercises
Review and Warmup
Answer 1.
\(a\hbox{, }A\hbox{, }x\hbox{, }y\hbox{, or }z\)
Answer 2.
Answer 1.
\(a\hbox{, }A\hbox{, }x\hbox{, }y\hbox{, or }z\)
Answer 2.
\({\text{years or months}}\)
Answer 1.
\(t\hbox{, }T\hbox{, }x\hbox{, }y\hbox{, or }z\)
Answer 2.
\({\text{hours or minutes}}\)
Skills Practice
Answer.
\(11\mathopen{}\left(x+14\right)\)
Answer.
\(3\mathopen{}\left(x+5\right) = 14\)
Applications
Challenge
1.9 Variables, Expressions, and Equations Chapter Review
Review Exercises for Chapter 1
Section 1: Variables and Evaluating Expressions
Answer 1.
\(t\hbox{, }T\hbox{, }x\hbox{, or }y\)
Answer 2.
\({\text{hours or minutes}}\)
Answer 1.
\(a\hbox{, }A\hbox{, }s\hbox{, }S\hbox{, }x\hbox{, or }y\)
Answer 2.
Section 2: Combining Like Terms
Answer.
\(\frac{64}{35}q+\frac{31}{5}k\)
Section 3: Comparison Symbols and Notation for Intervals
Answer 1.
\(\left\{x \mid x > -1\right\}\)
Answer 2.
\(\left(-1,\infty \right)\)
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,2\right)\right\}\)
Answer 2.
\(\left\{x \mid x < 2\right\}\)
Answer 1.
\(\left\{\mathrm{pH} \mid \mathrm{pH} < 7\right\}\)
Answer 2.
\(\left(-\infty ,7\right)\)
Section 4: Equations, Inequalities, and Solutions
Answer 1.
Answer 2.
Answer 3.
\(\text{No, it is not a solution.}\)
Answer 1.
Answer 2.
\(\text{Yes, it is a solution.}\)
Answer 1.
Answer 2.
Answer 3.
\(\text{No, it is not a solution.}\)
Answer 1.
Answer 2.
\(\text{No, it is not a solution.}\)
Answer 1.
Answer 2.
\(\text{No, it is not a solution.}\)
Answer 1.
Answer 2.
\(\text{No, it is not a solution.}\)
Section 5: Solving One-Step Equations
Section 6: Solving One-Step Inequalities
Answer 1.
\(\left\{\text{interval}, \left(-3,\infty \right)\right\}\)
Answer 2.
\(\left(-3,\infty \right)\)
Answer 3.
\(\left\{d \mid d > -3\right\}\)
Section 7: Algebraic Properties and Simplifying Expressions
Answer.
\(\left(z+3\right)\cdot 2\)
Answer.
\(-15X+\left(-24\right)\)
Section 8: Modeling with Equations and Inequalities
2 Linear Equations and Inequalities
2.1 Solving Multistep Linear Equations
2.1.6 Exercises
Review and Warmup
Answer.
\(\left\{\frac{9}{8}\right\}\)
Vocabulary
Skills Practice
Answer.
\(\left\{\frac{-1}{2}\right\}\)
Answer.
\(\left\{\frac{13}{6}\right\}\)
Answer.
\(\left\{\frac{7}{3}\right\}\)
Answer.
\(\left\{3.31818\right\}\)
Answer.
\(\left\{0.301075\right\}\)
Answer.
\(\left\{-0.366197\right\}\)
Answer.
\(\left\{\frac{11}{5}\right\}\)
Answer.
\(\left\{\frac{1}{11}\right\}\)
Answer.
\(\left\{\frac{31}{24}\right\}\)
Answer.
\(\left\{\frac{7}{12}\right\}\)
Answer.
\(\left\{\frac{1}{6}\right\}\)
Applications
2.2 Solving Multistep Linear Inequalities
2.2.4 Exercises
Review and Warmup
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,6\right)\right\}\)
Answer 2.
\(\left(-\infty ,6\right)\)
Answer 3.
\(\left\{s \mid s < 6\right\}\)
Answer 1.
\(\left\{\text{interval}, \left[-6,\infty \right)\right\}\)
Answer 2.
\(\left[-6,\infty \right)\)
Answer 3.
\(\left\{D \mid D\ge -6\right\}\)
Skills Practice
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,1\right]\right\}\)
Answer 2.
\(\left(-\infty ,1\right]\)
Answer 3.
\(\left\{P \mid P\le 1\right\}\)
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,5\right]\right\}\)
Answer 2.
\(\left(-\infty ,5\right]\)
Answer 3.
\(\left\{b \mid b\le 5\right\}\)
Answer 1.
\(\left\{\text{interval}, \left[-4,\infty \right)\right\}\)
Answer 2.
\(\left[-4,\infty \right)\)
Answer 3.
\(\left\{m \mid m\ge -4\right\}\)
Answer 1.
\(\left\{\text{interval}, \left[-1,\infty \right)\right\}\)
Answer 2.
\(\left[-1,\infty \right)\)
Answer 3.
\(\left\{x \mid x\ge -1\right\}\)
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,3\right]\right\}\)
Answer 2.
\(\left(-\infty ,3\right]\)
Answer 3.
\(\left\{J \mid J\le 3\right\}\)
Answer 1.
\(\left\{\text{interval}, \left[-6,\infty \right)\right\}\)
Answer 2.
\(\left[-6,\infty \right)\)
Answer 3.
\(\left\{V \mid V\ge -6\right\}\)
Answer 1.
\(\left\{\text{interval}, \left[-2,\infty \right)\right\}\)
Answer 2.
\(\left[-2,\infty \right)\)
Answer 3.
\(\left\{g \mid g\ge -2\right\}\)
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,2\right)\right\}\)
Answer 2.
\(\left(-\infty ,2\right)\)
Answer 3.
\(\left\{s \mid s < 2\right\}\)
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,6\right)\right\}\)
Answer 2.
\(\left(-\infty ,6\right)\)
Answer 3.
\(\left\{C \mid C < 6\right\}\)
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-3\right]\right\}\)
Answer 2.
\(\left(-\infty ,-3\right]\)
Answer 3.
\(\left\{P \mid P\le -3\right\}\)
Answer 1.
\(\left\{\text{interval}, \left[1,\infty \right)\right\}\)
Answer 2.
\(\left[1,\infty \right)\)
Answer 3.
\(\left\{b \mid b\ge 1\right\}\)
Answer 1.
\(\left\{\text{interval}, \left[5,\infty \right)\right\}\)
Answer 2.
\(\left[5,\infty \right)\)
Answer 3.
\(\left\{l \mid l\ge 5\right\}\)
Answer 1.
\(\left\{\text{interval}, \left(-4,\infty \right)\right\}\)
Answer 2.
\(\left(-4,\infty \right)\)
Answer 3.
\(\left\{x \mid x > -4\right\}\)
Answer 1.
\(\left\{\text{interval}, \left(-1,\infty \right)\right\}\)
Answer 2.
\(\left(-1,\infty \right)\)
Answer 3.
\(\left\{I \mid I > -1\right\}\)
Applications
Answer.
\(\left[8.09524,\infty \right)\)
Answer.
\(\left[10000,82608\right)\)
2.3 Equations and Inequalities with Fractions
2.3.5 Exercises
Review and Warmup
Skills Practice
Answer 1.
Answer 2.
\(\left\{\frac{37}{108}\right\}\)
Answer 1.
Answer 2.
\(\left\{\frac{-1}{3}\right\}\)
Answer 1.
Answer 2.
\(\left\{\frac{-8}{11}\right\}\)
Answer 1.
Answer 2.
\(\left\{\frac{-144}{5}\right\}\)
Answer 1.
Answer 2.
\(\left\{\frac{652}{15}\right\}\)
Answer 1.
Answer 2.
\(\left\{\frac{23}{49}\right\}\)
Answer 1.
Answer 2.
\(\left\{\frac{261}{100}\right\}\)
Answer 1.
Answer 2.
\(\left\{\frac{1}{216}\right\}\)
Answer 1.
Answer 2.
\(\left\{\frac{7}{41}\right\}\)
Answer 1.
Answer 2.
\(\left\{x \mid x\ge \frac{8}{33}\right\}\)
Answer 3.
\(\left[{\frac{8}{33}},\infty \right)\)
Answer 1.
Answer 2.
\(\left\{x \mid x\le \frac{32}{7}\right\}\)
Answer 3.
\(\left(-\infty ,{\frac{32}{7}}\right]\)
Answer 1.
Answer 2.
\(\left\{x \mid x > \frac{-447}{35}\right\}\)
Answer 3.
\(\left(-{\frac{447}{35}},\infty \right)\)
Answer 1.
Answer 2.
\(\left\{x \mid x\ge \frac{49}{45}\right\}\)
Answer 3.
\(\left[{\frac{49}{45}},\infty \right)\)
Answer 1.
Answer 2.
\(\left\{x \mid x > \frac{732}{485}\right\}\)
Answer 3.
\(\left({\frac{732}{485}},\infty \right)\)
Applications
Challenge
2.4 Special Solution Sets
2.4.4 Exercises
Notation
Answer.
\(\text{no real solutions}\)
Skills Practice
Answer.
\(\text{no real solutions}\)
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
Answer.
\(\text{no real solutions}\)
Answer.
\(\text{no real solutions}\)
Answer.
\(\text{no real solutions}\)
Answer.
\(\text{no real solutions}\)
Answer.
\(\text{no real solutions}\)
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
Answer.
\(\text{no real solutions}\)
Answer.
\(\text{no real solutions}\)
Answer.
\(\text{no real solutions}\)
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
Answer.
\(\text{no real solutions}\)
Answer.
\(\text{no real solutions}\)
Answer.
\(\text{no real solutions}\)
Challenge
Answer 1.
Answer 2.
\(6\mathopen{}\left(x+4\right)\)
2.5 Isolating a Linear Variable
2.5.3 Exercises
Skills Practice
Answer.
\(\left\{\frac{3}{8}\right\}\)
Answer.
\(i = d\mathopen{}\left(W-q\right)\)
Answer.
\(y = -{\frac{9}{7}}x+8\)
Answer.
\(y = -x+-{\frac{7}{8}}\)
Answer.
\(y = {\frac{13}{5}}x+-{\frac{148}{25}}\)
Applications
Answer.
\(h = \frac{V}{\pi r^{2}}\)
2.6 Linear Equations and Inequalities Chapter Review
Review Exercises for Chapter 2
Section 1: Solving Multistep Linear Equations
Answer.
\(\left\{0.910112\right\}\)
Answer.
\(\left\{\frac{-37}{21}\right\}\)
Answer.
\({\frac{20}{3}}\ {\rm yr}\)
Section 2: Solving Multistep Linear Inequalities
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,3\right)\right\}\)
Answer 2.
\(\left(-\infty ,3\right)\)
Answer 3.
\(\left\{u \mid u < 3\right\}\)
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-6\right]\right\}\)
Answer 2.
\(\left(-\infty ,-6\right]\)
Answer 3.
\(\left\{F \mid F\le -6\right\}\)
Answer 1.
\(\left\{\text{interval}, \left[-2,\infty \right)\right\}\)
Answer 2.
\(\left[-2,\infty \right)\)
Answer 3.
\(\left\{R \mid R\ge -2\right\}\)
Section 3: Equations and Inequalities with Fractions
Answer 1.
Answer 2.
\(\left\{\frac{-81}{35}\right\}\)
Answer 1.
Answer 2.
\(\left\{x \mid x\le \frac{-19}{35}\right\}\)
Answer 3.
\(\left(-\infty ,-{\frac{19}{35}}\right]\)
Answer 1.
Answer 2.
\(\left\{x \mid x\ge \frac{-71}{73}\right\}\)
Answer 3.
\(\left[-{\frac{71}{73}},\infty \right)\)
Section 4: Special Solution Sets
Answer.
\(\text{no real solutions}\)
Answer.
\(\text{no real solutions}\)
Answer.
\(\text{no real solutions}\)
Answer.
\(\text{no real solutions}\)
Section 5: Isolating a Linear Variable
3 Graphing Lines
3.1 Cartesian Coordinates
Exercises
Answer 1.
Answer 2.
Answer 3.
Answer 4.
Answer.
\(\left\{\text{point}, \left(2,3\right)\right\}, \left\{\text{point}, \left(1,-2\right)\right\}, \left\{\text{point}, \left(0,7\right)\right\}, \left\{\text{point}, \left(-4,0\right)\right\}\)
Answer.
\(\left\{\text{point}, \left(4,-1.33333\right)\right\}, \left\{\text{point}, \left(2.33333,2\right)\right\}\)
Answer.
\(\left\{\text{point}, \left(-4.75,0.5\right)\right\}, \left\{\text{point}, \left(-2.75,-2.5\right)\right\}\)
Answer.
\(\left\{\text{point}, \left(127,124\right)\right\}, \left\{\text{point}, \left(146,172\right)\right\}\)
Answer.
\(\left\{\text{fill}, \left(1,-1\right)\right\}, \left\{\text{fill}, \left(-1,-1\right)\right\}\)
Answer.
\(\left\{\text{fill}, \left(1,1\right)\right\}, \left\{\text{fill}, \left(-1,-1\right)\right\}\)
3.2 Graphing Equations
Exercises
Skills Practice
Answer.
\(\text{Choice 3, Choice 4}\)
Answer.
\(\text{Choice 3, Choice 4}\)
Answer.
\(\text{Choice 1, Choice 3, Choice 4}\)
Answer.
\(\text{Choice 1, Choice 3}\)
Answer 1.
\(8;\,\left(-2,8\right);\,5;\,\left(-1,5\right);\,2;\,\left(0,2\right);\,-1;\,\left(1,-1\right);\,-4;\,\left(2,-4\right)\)
Answer 2.
\(\left\{\text{point}, \left(-2,8\right)\right\}, \left\{\text{point}, \left(-1,5\right)\right\}, \left\{\text{point}, \left(0,2\right)\right\}, \left\{\text{point}, \left(1,-1\right)\right\}, \left\{\text{point}, \left(2,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-2,8\right), \left(-1,5\right)\right\}\)
Answer 1.
\(-5;\,\left(-8,-5\right);\,-4;\,\left(-4,-4\right);\,-3;\,\left(0,-3\right);\,-2;\,\left(4,-2\right);\,-1;\,\left(8,-1\right)\)
Answer 2.
\(\left\{\text{point}, \left(-8,-5\right)\right\}, \left\{\text{point}, \left(-4,-4\right)\right\}, \left\{\text{point}, \left(0,-3\right)\right\}, \left\{\text{point}, \left(4,-2\right)\right\}, \left\{\text{point}, \left(8,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-5\right), \left(-4,-4\right)\right\}\)
Answer 1.
\(2;\,\left(-2,2\right);\,3;\,\left(-1,3\right);\,2;\,\left(0,2\right);\,-1;\,\left(1,-1\right);\,-6;\,\left(2,-6\right)\)
Answer 2.
\(\left\{\text{point}, \left(-2,2\right)\right\}, \left\{\text{point}, \left(-1,3\right)\right\}, \left\{\text{point}, \left(0,2\right)\right\}, \left\{\text{point}, \left(1,-1\right)\right\}, \left\{\text{point}, \left(2,-6\right)\right\}, \left\{\text{quadratic}, \text{solid}, \left(-2,2\right), \left(-1,3\right), \left(0,2\right)\right\}\)
Answer 1.
\(-5;\,\left(-2,-5\right);\,-2;\,\left(-1,-2\right);\,-3;\,\left(0,-3\right);\,-2;\,\left(1,-2\right);\,7;\,\left(2,7\right)\)
Answer 2.
\(\left\{\text{point}, \left(-2,-5\right)\right\}, \left\{\text{point}, \left(-1,-2\right)\right\}, \left\{\text{point}, \left(0,-3\right)\right\}, \left\{\text{point}, \left(1,-2\right)\right\}, \left\{\text{point}, \left(2,7\right)\right\}, \left\{\text{cubic}, \text{solid}, \left(-2,-5\right), \left(-1,-2\right), \left(0,-3\right), \left(1,-2\right)\right\}\)
Answer.
\(\text{Choice 1, Choice 2, Choice 6}\)
Applications
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,800\right), \left(1,820\right)\right\}\)
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
Applications
Answer.
\(6462.9\,\frac{\text{person}}{\text{yr}}\)
Answer.
\(617\,\frac{\text{person}}{\text{yr}}\)
Answer.
\(\left[2003\right], \left[2019\right], \left[2020\right], \left[2021\right]\)
Answer.
\(\left[2006,2016\right]\)
Answer.
\(10203.9\,\frac{\text{person}}{\text{yr}}\)
3.4 Slope
3.4.5 Exercises
Skills Practice
Answer.
\(\left\{\text{line}, \text{solid}, \left(3,-1\right), \left(5,2\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(-2,1\right), \left(0,-2\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(-8,-8\right), \left(-5,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-7\right), \left(-5,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-6\right), \left(-5,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-5\right), \left(-5,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-4\right), \left(-5,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-8\right), \left(-4,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-7\right), \left(-4,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-6\right), \left(-4,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-5\right), \left(-4,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-4\right), \left(-4,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-8\right), \left(-3,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-7\right), \left(-3,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-6\right), \left(-3,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-5\right), \left(-3,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-4\right), \left(-3,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,-8\right), \left(-2,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,-7\right), \left(-2,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,-6\right), \left(-2,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,-5\right), \left(-2,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,-4\right), \left(-2,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,-8\right), \left(-1,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,-7\right), \left(-1,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,-6\right), \left(-1,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,-5\right), \left(-1,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,-4\right), \left(-1,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-3,-8\right), \left(0,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-3,-7\right), \left(0,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-3,-6\right), \left(0,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-3,-5\right), \left(0,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-3,-4\right), \left(0,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-2,-8\right), \left(1,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-2,-7\right), \left(1,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-2,-6\right), \left(1,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-2,-5\right), \left(1,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-2,-4\right), \left(1,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-1,-8\right), \left(2,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-1,-7\right), \left(2,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-1,-6\right), \left(2,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-1,-5\right), \left(2,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-1,-4\right), \left(2,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,-8\right), \left(3,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,-7\right), \left(3,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,-6\right), \left(3,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,-5\right), \left(3,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,-4\right), \left(3,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(1,-8\right), \left(4,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(1,-7\right), \left(4,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(1,-6\right), \left(4,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(1,-5\right), \left(4,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(1,-4\right), \left(4,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(2,-8\right), \left(5,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(2,-7\right), \left(5,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(2,-6\right), \left(5,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(2,-5\right), \left(5,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(2,-4\right), \left(5,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(3,-8\right), \left(6,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(3,-7\right), \left(6,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(3,-6\right), \left(6,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(3,-5\right), \left(6,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(3,-4\right), \left(6,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(4,-8\right), \left(7,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(4,-7\right), \left(7,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(4,-6\right), \left(7,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(4,-5\right), \left(7,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(4,-4\right), \left(7,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(5,-8\right), \left(8,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(5,-7\right), \left(8,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(5,-6\right), \left(8,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(5,-5\right), \left(8,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(5,-4\right), \left(8,1\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(-5,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-1\right), \left(-5,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,0\right), \left(-5,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,1\right), \left(-5,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,2\right), \left(-5,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,3\right), \left(-5,8\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(-4,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-1\right), \left(-4,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,0\right), \left(-4,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,1\right), \left(-4,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,2\right), \left(-4,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,3\right), \left(-4,8\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(-3,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-1\right), \left(-3,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,0\right), \left(-3,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,1\right), \left(-3,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,2\right), \left(-3,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,3\right), \left(-3,8\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(-8,-9\right), \left(-5,-10\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-8\right), \left(-5,-9\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-7\right), \left(-5,-8\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-6\right), \left(-5,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-5\right), \left(-5,-6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-4\right), \left(-5,-5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-3\right), \left(-5,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-2\right), \left(-5,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-1\right), \left(-5,-2\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(-5,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,2\right), \left(-5,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,3\right), \left(-5,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,4\right), \left(-5,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,5\right), \left(-5,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,6\right), \left(-5,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,7\right), \left(-5,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,8\right), \left(-5,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,9\right), \left(-5,8\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-9\right), \left(-4,-10\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-8\right), \left(-4,-9\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-7\right), \left(-4,-8\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-6\right), \left(-4,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-5\right), \left(-4,-6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-4\right), \left(-4,-5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-3\right), \left(-4,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-2\right), \left(-4,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-1\right), \left(-4,-2\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(-4,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,2\right), \left(-4,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,3\right), \left(-4,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,4\right), \left(-4,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,5\right), \left(-4,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,6\right), \left(-4,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,7\right), \left(-4,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,8\right), \left(-4,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,9\right), \left(-4,8\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-9\right), \left(-3,-10\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-8\right), \left(-3,-9\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-7\right), \left(-3,-8\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-6\right), \left(-3,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-5\right), \left(-3,-6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-4\right), \left(-3,-5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-3\right), \left(-3,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-2\right), \left(-3,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-1\right), \left(-3,-2\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(-3,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,2\right), \left(-3,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,3\right), \left(-3,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,4\right), \left(-3,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,5\right), \left(-3,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,6\right), \left(-3,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,7\right), \left(-3,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,8\right), \left(-3,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,9\right), \left(-3,8\right)\right\}\)
Applications
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.
\(-500\ {\textstyle\frac{\rm\mathstrut ft}{\rm\mathstrut h}}\)
Answer.
\(-10\ {\textstyle\frac{\rm\mathstrut ml}{\rm\mathstrut min}}\)
Challenge
3.5 Slope-Intercept Form
3.5.7 Exercises
Skills Practice
Answer.
\(y = -{\frac{3}{5}}x+4\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,3\right), \left(1,8\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,5\right), \left(1,3\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,2\right), \left(-3,3\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-3\right), \left(4,-2\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,0\right), \left(9,8\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-4\right), \left(9,-2\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-4\right), \left(1,-3\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,1\right), \left(1,0\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-5\right), \left(9,-12\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-3\right), \left(10,6\right)\right\}\)
Answer.
\(y = -{\frac{8}{7}}x-8\)
Answer.
\(y = {\frac{11}{17}}x+44\)
Applications
Answer 1.
Answer 2.
Answer 3.
Answer 1.
Answer 2.
Answer 3.
Answer 1.
Answer 2.
Answer 3.
Answer 1.
Answer 2.
Answer 3.
3.6 Point-Slope Form
3.6.5 Exercises
Skills Practice
Answer.
\(y = 7\mathopen{}\left(x-4\right)+9\)
Answer.
\(y = 9\mathopen{}\left(x+6\right)-7\)
Answer.
\(y = -5.1\mathopen{}\left(x-6\right)-4\)
Answer.
\(y = 5\mathopen{}\left(x-3\right)+6\hbox{ or }y = 5\mathopen{}\left(x-9\right)+36\)
Answer.
\(y = -3\mathopen{}\left(x-2\right)-6\hbox{ or }y = -3\mathopen{}\left(x+5\right)+15\)
Answer.
\(y = -\frac{1}{4}\mathopen{}\left(x-7\right)+8\hbox{ or }y = -\frac{1}{4}\mathopen{}\left(x-23\right)+4\)
Answer.
\(y = \frac{8}{9}\mathopen{}\left(x+8\right)-5\hbox{ or }y = \frac{8}{9}\mathopen{}\left(x+71\right)-61\)
Answer.
\(y = \frac{4}{5}x-\frac{18}{5}\)
Answer.
\(y = \frac{5}{3}\mathopen{}\left(x+7\right)-7\hbox{, }y = \frac{5}{3}\mathopen{}\left(x+4\right)-2\hbox{, or }y = \frac{5}{3}\mathopen{}\left(x+1\right)+3\)
Answer.
\(y = 5-\frac{7}{8}\mathopen{}\left(x+5\right)\hbox{ or }y = -\left(\frac{7}{8}\mathopen{}\left(x-3\right)+2\right)\)
Answer.
\(y = 125\mathopen{}\left(x-8\right)+150\hbox{ or }y = 125\mathopen{}\left(x-10\right)+400\)
Answer.
\(y = \frac{93}{7}\mathopen{}\left(x-9\right)+345\hbox{ or }y = \frac{93}{7}\mathopen{}\left(x-2\right)+252\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(2,5\right), \left(3,8\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(3,-2\right), \left(4,2\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(-3,-7\right), \left(-1,-6\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(-8,9\right), \left(-5,5\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(-3,-8\right), \left(7,0\right)\right\}\)
Applications
Answer 1.
\(y = 0.03\mathopen{}\left(x-260\right)+22.8\)
Answer 2.
Answer 3.
Answer 1.
\(y = 0.18\mathopen{}\left(x-12\right)+19.26\)
Answer 2.
Answer 3.
Answer 1.
\(y = -38000\mathopen{}\left(x-2\right)+550000\hbox{ or }y = -38000\mathopen{}\left(x-5\right)+436000\)
Answer 2.
Answer 3.
Answer 1.
\(y = -4.3\mathopen{}\left(x-5\right)+189.2\hbox{ or }y = -4.3\mathopen{}\left(x-17\right)+137.6\)
Answer 2.
Answer 3.
3.7 Standard Form
3.7.5 Exercises
Review and Warmup
Answer.
\(y = -{\frac{3}{2}}x+10\)
Answer.
\(y = -x+-{\frac{116}{39}}\)
Skills Practice
Answer 1.
Answer 2.
Answer 3.
Answer 1.
Answer 2.
Answer 3.
Answer 1.
\(\left(\frac{7}{5},0\right)\)
Answer 2.
\(\left(0,\frac{7}{8}\right)\)
Answer 3.
Answer 1.
\(\left(\frac{31}{76},0\right)\)
Answer 2.
\(\left(0,\frac{-31}{56}\right)\)
Answer 3.
Answer 1.
\(\left(\frac{1}{2},0\right)\)
Answer 2.
\(\left(0,\frac{9}{7}\right)\)
Answer 3.
Answer 1.
\(\left(-3.14286,0\right)\)
Answer 2.
\(\left(0,0.741573\right)\)
Answer 3.
Answer.
\(\left\{\text{line}, \text{solid}, \left(8,0\right), \left(0,9\right)\right\}, \left\{\text{point}, \left(8,0\right)\right\}, \left\{\text{point}, \left(0,9\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(2,0\right), \left(0,-5\right)\right\}, \left\{\text{point}, \left(2,0\right)\right\}, \left\{\text{point}, \left(0,-5\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(-4,0\right), \left(0,-7\right)\right\}, \left\{\text{point}, \left(-4,0\right)\right\}, \left\{\text{point}, \left(0,-7\right)\right\}\)
Applications
Challenge
Answer 1.
Answer 2.
Answer 3.
Answer 1.
Answer 2.
Answer 3.
3.8 Geometry of Lines
3.8.5 Exercises
Review and Warmup
Answer.
\(y = 6\mathopen{}\left(x-4\right)+9\hbox{ or }y = 6\mathopen{}\left(x-8\right)+33\)
Answer.
\(y = -\frac{3}{2}\mathopen{}\left(x-6\right)+4\hbox{ or }y = -\frac{3}{2}\mathopen{}\left(x+2\right)+16\)
Answer.
\(\text{Choice 3, Choice 4}\)
Answer.
\(\text{Choice 1, Choice 4}\)
Skills Practice
Answer 1.
\(3;\,-2;\,\left(3,-2\right);\,3;\,-1;\,\left(3,-1\right);\,3;\,0;\,\left(3,0\right);\,3;\,1;\,\left(3,1\right);\,3;\,2;\,\left(3,2\right)\)
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(3,-2\right), \left(3,-1\right)\right\}\)
Answer 1.
\(-2;\,4;\,\left(-2,4\right);\,-1;\,4;\,\left(-1,4\right);\,0;\,4;\,\left(0,4\right);\,1;\,4;\,\left(1,4\right);\,2;\,4;\,\left(2,4\right)\)
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(-2,4\right), \left(-1,4\right)\right\}\)
Answer.
\(\text{distinct and parallel}\)
Answer.
\(\text{none of the above}\)
Answer 1.
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(7,0\right), \left(5,-7\right)\right\}\)
Answer 1.
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(0,8\right), \left(6,-1\right)\right\}\)
Answer 1.
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(-9,4\right), \left(-9,9\right)\right\}\)
Answer 1.
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(7,8\right), \left(-4,8\right)\right\}\)
3.9 Strategies for Graphing Lines
3.9.5 Exercises
Answer 1.
\(4;\,\left(-2,4\right);\,1;\,\left(-1,1\right);\,-2;\,\left(0,-2\right);\,-5;\,\left(1,-5\right);\,-8;\,\left(2,-8\right)\)
Answer 2.
\(\left\{\text{point}, \left(-2,4\right)\right\}, \left\{\text{point}, \left(-1,1\right)\right\}, \left\{\text{point}, \left(0,-2\right)\right\}, \left\{\text{point}, \left(1,-5\right)\right\}, \left\{\text{point}, \left(2,-8\right)\right\}, \left\{\text{line}, \text{solid}, \left(-2,4\right), \left(-1,1\right)\right\}\)
Answer 1.
\(-9;\,\left(-8,-9\right);\,-6;\,\left(-4,-6\right);\,-3;\,\left(0,-3\right);\,0;\,\left(4,0\right);\,3;\,\left(8,3\right)\)
Answer 2.
\(\left\{\text{point}, \left(-8,-9\right)\right\}, \left\{\text{point}, \left(-4,-6\right)\right\}, \left\{\text{point}, \left(0,-3\right)\right\}, \left\{\text{point}, \left(4,0\right)\right\}, \left\{\text{point}, \left(8,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-9\right), \left(-4,-6\right)\right\}\)
Answer 1.
\(1;\,-2;\,\left(1,-2\right);\,1;\,-1;\,\left(1,-1\right);\,1;\,0;\,\left(1,0\right);\,1;\,1;\,\left(1,1\right);\,1;\,2;\,\left(1,2\right)\)
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(1,-2\right), \left(1,-1\right)\right\}\)
Answer 1.
\(-2;\,6;\,\left(-2,6\right);\,-1;\,6;\,\left(-1,6\right);\,0;\,6;\,\left(0,6\right);\,1;\,6;\,\left(1,6\right);\,2;\,6;\,\left(2,6\right)\)
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(-2,6\right), \left(-1,6\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(2,0\right), \left(0,5\right)\right\}, \left\{\text{point}, \left(2,0\right)\right\}, \left\{\text{point}, \left(0,5\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(3,0\right), \left(0,-7\right)\right\}, \left\{\text{point}, \left(3,0\right)\right\}, \left\{\text{point}, \left(0,-7\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(-5,0\right), \left(0,-9\right)\right\}, \left\{\text{point}, \left(-5,0\right)\right\}, \left\{\text{point}, \left(0,-9\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-2\right), \left(1,2\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-3\right), \left(1,-8\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-5\right), \left(-2,-4\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,2\right), \left(3,3\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-3\right), \left(7,3\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,5\right), \left(1,6\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-4\right), \left(3,-6\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(2,4\right), \left(3,9\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(3,-5\right), \left(4,-1\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(-8,-2\right), \left(-1,1\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(4,-3\right), \left(12,-6\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(7,-2\right), \left(17,-9\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-5\right), \left(1,-2\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-3\right), \left(7,-9\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(-6,-7\right), \left(2,0\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(2,0\right), \left(0,9\right)\right\}, \left\{\text{point}, \left(2,0\right)\right\}, \left\{\text{point}, \left(0,9\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(-5,-2\right), \left(-5,-1\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(-2,-1\right), \left(-1,-1\right)\right\}\)
3.10 Graphing Lines Chapter Review
Review Exercises for Chapter 3
Section 1: Cartesian Coordinates
Answer 1.
Answer 2.
Answer 3.
Answer 4.
Answer.
\(\left\{\text{point}, \left(1,0\right)\right\}, \left\{\text{point}, \left(5,3\right)\right\}, \left\{\text{point}, \left(0,8\right)\right\}, \left\{\text{point}, \left(-3,2\right)\right\}\)
Answer.
\(\left\{\text{fill}, \left(1,1\right)\right\}, \left\{\text{fill}, \left(1,-1\right)\right\}\)
Section 2: Graphing Equations
Answer.
\(\text{Choice 2, Choice 3}\)
Answer 1.
\(12;\,\left(-2,12\right);\,1;\,\left(-1,1\right);\,-2;\,\left(0,-2\right);\,-3;\,\left(1,-3\right);\,-8;\,\left(2,-8\right)\)
Answer 2.
\(\left\{\text{point}, \left(-2,12\right)\right\}, \left\{\text{point}, \left(-1,1\right)\right\}, \left\{\text{point}, \left(0,-2\right)\right\}, \left\{\text{point}, \left(1,-3\right)\right\}, \left\{\text{point}, \left(2,-8\right)\right\}, \left\{\text{cubic}, \text{solid}, \left(-2,12\right), \left(-1,1\right), \left(0,-2\right), \left(1,-3\right)\right\}\)
Section 3: Exploring Two-Variable Data and Rate of Change
Section 4: Slope
Answer.
\(\left\{\text{line}, \text{solid}, \left(-8,-8\right), \left(-3,-6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-7\right), \left(-3,-5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-8\right), \left(-2,-6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-7\right), \left(-2,-5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-8\right), \left(-1,-6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-7\right), \left(-1,-5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,-8\right), \left(0,-6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,-7\right), \left(0,-5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,-8\right), \left(1,-6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,-7\right), \left(1,-5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-3,-8\right), \left(2,-6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-3,-7\right), \left(2,-5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-2,-8\right), \left(3,-6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-2,-7\right), \left(3,-5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-1,-8\right), \left(4,-6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-1,-7\right), \left(4,-5\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,-8\right), \left(5,-6\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,-7\right), \left(5,-5\right)\right\}, \left\{\text{line}, \text{solid}, \left(1,-8\right), \left(6,-6\right)\right\}, \left\{\text{line}, \text{solid}, \left(1,-7\right), \left(6,-5\right)\right\}, \left\{\text{line}, \text{solid}, \left(2,-8\right), \left(7,-6\right)\right\}, \left\{\text{line}, \text{solid}, \left(2,-7\right), \left(7,-5\right)\right\}, \left\{\text{line}, \text{solid}, \left(3,-8\right), \left(8,-6\right)\right\}, \left\{\text{line}, \text{solid}, \left(3,-7\right), \left(8,-5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-6\right), \left(-3,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-5\right), \left(-3,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-4\right), \left(-3,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-3\right), \left(-3,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-2\right), \left(-3,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-1\right), \left(-3,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,0\right), \left(-3,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,1\right), \left(-3,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,2\right), \left(-3,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,3\right), \left(-3,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,4\right), \left(-3,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,5\right), \left(-3,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,6\right), \left(-3,8\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-6\right), \left(-2,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-5\right), \left(-2,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-4\right), \left(-2,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-3\right), \left(-2,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-2\right), \left(-2,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-1\right), \left(-2,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,0\right), \left(-2,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,1\right), \left(-2,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,2\right), \left(-2,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,3\right), \left(-2,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,4\right), \left(-2,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,5\right), \left(-2,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,6\right), \left(-2,8\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-6\right), \left(-1,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-5\right), \left(-1,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-4\right), \left(-1,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-3\right), \left(-1,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-2\right), \left(-1,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-1\right), \left(-1,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,0\right), \left(-1,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,1\right), \left(-1,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,2\right), \left(-1,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,3\right), \left(-1,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,4\right), \left(-1,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,5\right), \left(-1,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,6\right), \left(-1,8\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,-6\right), \left(0,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,-5\right), \left(0,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,-4\right), \left(0,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,-3\right), \left(0,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,-2\right), \left(0,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,-1\right), \left(0,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,0\right), \left(0,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,1\right), \left(0,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,2\right), \left(0,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,3\right), \left(0,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,4\right), \left(0,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,5\right), \left(0,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,6\right), \left(0,8\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,-6\right), \left(1,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,-5\right), \left(1,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,-4\right), \left(1,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,-3\right), \left(1,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,-2\right), \left(1,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,-1\right), \left(1,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,0\right), \left(1,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,1\right), \left(1,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,2\right), \left(1,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,3\right), \left(1,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,4\right), \left(1,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,5\right), \left(1,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,6\right), \left(1,8\right)\right\}\)
Answer.
\(-10\ {\textstyle\frac{\rm\mathstrut ml}{\rm\mathstrut min}}\)
Section 5: Slope-Intercept Form
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-5\right), \left(-3,-4\right)\right\}\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-3\right), \left(5,-9\right)\right\}\)
Answer.
\(y = -{\frac{6}{5}}x+5\)
Answer 1.
Answer 2.
Answer 3.
Section 6: Point-Slope Form
Answer.
\(y = 7\mathopen{}\left(x-8\right)+9\)
Answer.
\(y = 8\mathopen{}\left(x-2\right)+7\hbox{ or }y = 8\mathopen{}\left(x-3\right)+15\)
Answer.
\(y = 6-\frac{7}{4}\mathopen{}\left(x+2\right)\hbox{ or }y = -\left(\frac{7}{4}\mathopen{}\left(x-2\right)+1\right)\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(4,5\right), \left(5,7\right)\right\}\)
Answer 1.
\(y = -43000\mathopen{}\left(x-2\right)+624000\)
Answer 2.
Answer 3.
Answer 1.
\(y = 0.3\mathopen{}\left(x-15\right)+20.2\hbox{ or }y = 0.3\mathopen{}\left(x-17\right)+20.8\)
Answer 2.
Answer 3.
Section 7: Standard Form
Answer 1.
\(\left(3.42857,0\right)\)
Answer 2.
\(\left(0,-1.10345\right)\)
Answer 3.
Answer.
\(\left\{\text{line}, \text{solid}, \left(-7,0\right), \left(0,-5\right)\right\}, \left\{\text{point}, \left(-7,0\right)\right\}, \left\{\text{point}, \left(0,-5\right)\right\}\)
Section 8: Geometry of Lines
Answer 1.
\(-2;\,7;\,\left(-2,7\right);\,-1;\,7;\,\left(-1,7\right);\,0;\,7;\,\left(0,7\right);\,1;\,7;\,\left(1,7\right);\,2;\,7;\,\left(2,7\right)\)
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(-2,7\right), \left(-1,7\right)\right\}\)
Answer.
\(\text{none of the above}\)
4 Systems of Two Linear Equations
4.1 Solving a System by Graphing
4.1.5 Exercises
Review
Answer.
\(\text{Choice 1, Choice 3, Choice 5}\)
Skills Practice
Answer.
\(\text{Yes, it is a solution.}\)
Answer.
\(\text{No, it is not a solution.}\)
Answer.
\(\text{No, it is not a solution.}\)
Answer 1.
Answer 2.
\(\text{None of the above}\)
Answer 1.
\(\text{Infinitely many}\)
Answer 2.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(0,-9\right), \left(1,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,9\right), \left(1,-4\right)\right\}\)
Answer 2.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(8,9\right), \left(10,16\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,1\right), \left(6,2\right)\right\}\)
Answer 2.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(3,-2\right), \left(8,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(6,9\right), \left(11,17\right)\right\}\)
Answer 2.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(-4,0\right), \left(0,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(8,0\right), \left(0,-4\right)\right\}\)
Answer 2.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(-2,0\right), \left(0,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,-1\right), \left(0,5\right)\right\}\)
Answer 2.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(2,0\right), \left(0,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(2,-8\right), \left(0,-4\right)\right\}\)
Answer 2.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(4,0\right), \left(0,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(3,-3\right), \left(-5,-9\right)\right\}\)
Answer 2.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(-5,0\right), \left(0,1\right)\right\}\)
Answer 2.
\(\text{infinitely many solutions}\)
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(0,3\right), \left(2,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(1,-5\right), \left(2,-7\right)\right\}\)
Answer 2.
\(\text{infinitely many solutions}\)
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(0,1\right), \left(1,9\right)\right\}\)
Answer 2.
Applications
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,80\right), \left(56,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,68\right), \left(68,0\right)\right\}\)
Answer 1.
Answer 2.
\(d = 150+\left(-12\right)t\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,0\right), \left(1,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,150\right), \left(1,138\right)\right\}\)
4.2 Substitution
4.2.5 Exercises
Skills Practice
Answer.
\(\text{infinitely many solutions}\)
Answer.
\(D = -{\frac{1}{5}}, q = -{\frac{31}{5}}\)
Answer.
\(\text{infinitely many solutions}\)
Answer.
\(c = {\frac{3}{2}}, X = {\frac{67}{2}}\)
Answer.
\(m = -{\frac{74}{7}}, l = {\frac{17}{7}}\)
Answer.
\(y = {\frac{35}{9}}, B = -{\frac{17}{3}}\)
Answer.
\(J = -{\frac{50}{3}}, S = 6\)
Answer.
\(h = -0.333333, x = 5.46667\)
Answer.
\(s = 0.436636, N = -0.819582\)
Answer.
\(D = {\frac{19}{12}}, d = {\frac{16}{15}}\)
Answer.
\(Q = {\frac{26}{15}}, s = {\frac{19}{9}}\)
Answer.
\(b = -{\frac{5}{2}}, J = {\frac{3}{2}}\)
Answer.
\(x = -{\frac{23}{9}}, n = -{\frac{2}{27}}\)
Answer 1.
\(J = {\frac{135}{4}}, D = -{\frac{15}{2}}\)
Answer 2.
Answer.
\(\text{infinitely many solutions}\)
Applications
Answer 1.
Answer 2.
Answer 3.
Answer 4.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
4.3 Elimination
4.3.5 Exercises
Skills Practice
Answer.
\(P = {\frac{3}{2}}, S = {\frac{21}{2}}\)
Answer.
\(b = {\frac{77}{6}}, i = -{\frac{25}{3}}\)
Answer.
\(x = -{\frac{195}{28}}, N = -{\frac{100}{7}}\)
Answer.
\(\text{infinitely many solutions}\)
Answer.
\(\text{infinitely many solutions}\)
Applications
Answer 1.
Answer 2.
Answer 3.
Answer 4.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
Challenge
4.4 Systems of Two Linear Equations Chapter Review
Review Exercises for Chapter 4
Section 1: Solving a System by Graphing
Answer.
\(\text{Yes, it is a solution.}\)
Answer 1.
\(\text{Infinitely many}\)
Answer 2.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(-3,0\right), \left(0,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(3,3\right), \left(-6,-5\right)\right\}\)
Answer 2.
Answer 1.
Answer 2.
\(d = 65+\left(-10\right)t\)
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,0\right), \left(1,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,65\right), \left(1,55\right)\right\}\)
Section 2: Substitution
Answer.
\(\text{infinitely many solutions}\)
Answer.
\(f = 0.0714286, j = 0.385714\)
Answer.
\(r = -4, y = -{\frac{11}{3}}\)
Answer 1.
Answer 2.
Answer 3.
\(5.83333\ {\rm months}\)
Answer 4.
Answer 1.
Answer 2.
Answer 3.
Answer 4.
Section 3: Elimination
Answer 1.
Answer 2.
Answer 3.
Answer 4.
