Open Resources for Community College Algebra

Simplify algebraic expressions using the distributive, commutative, and associative properties.

Evaluate algebraic expressions.

Translate phrases and sentences into algebraic expressions and equations, and vice versa.

Distinguish between factors and terms.

Distinguish between evaluating expressions, simplifying expressions, and solving equations.

Identify linear equations and inequalities in one variable.

Use the definition of a solution to an equation or inequality to check if a given value is a solution.

Solve linear equations, including proportions, and non-compound linear inequalities symbolically.

Express inequality solution sets graphically and with interval notation.

Solve an equation for a specified variable in terms of other variables.

Solve applications in which two values are unknown but their total is known; for example, a 10-foot board cut into two pieces where one piece is 2.5 feet longer than the other piece.

Plot points on the Cartesian coordinate system, including pairs of values from a table.

Determine coordinates of points by reading a Cartesian graph.

Create a table of values from an equation or application. Make a plot from the table. When appropriate, correctly identify the independent variable with the horizontal axis and the dependent variable with the vertical axis.

Classify points by quadrant or as points on an axis; identify the origin.

Label and scale axes on all graphs.

Create graphs where the axes are required to have different scales (e.g. \(-10\) to \(10\) on the horizontal axis and \(-1000\) to \(1000\) on the vertical axis).

Interpret graphs, intercepts and other points in the context of an application. Express intercepts as ordered pairs.

Create tables and graphs with labels that communicate the context of an application problem and its dependent and independent quantities.

Write and interpret a slope as a rate of change in context (include the unit of the slope).

Find the slope of a line from a graph, from two points, and from a table of values.

Find the slope from all forms of a linear equation.

Given the graph of a line, identify the slope as positive, negative, zero, or undefined. Given two non-vertical lines, identify the line with greater slope.

Identify a linear equation in two variables.

Manipulate a linear equation into slope-intercept form; identify the slope and the vertical intercept given a linear equation.

Recognize equations of horizontal and vertical lines and identify their slopes as zero or undefined.

Write the equation of a line in slope-intercept form.

Write the equation of a line in point-slope form.

Graph a line with a known point and slope.

Emphasize that the graph of a line is a visual representation of the solution set to a linear equation.

Given a linear equation, find at least three ordered pairs that satisfy the equation and graph the line using those ordered pairs.

Given an equation in slope-intercept form, plot its graph using the slope and vertical intercept.

Given an equation in point-slope form, plot its graph using the slope and the suggested point.

Given an equation in standard form, plot its graph by calculating horizontal and vertical intercepts, and check with a third point.

Given an equation for a vertical or horizontal line, plot its graph.

Create and graph a linear model based on data and make predictions based upon the model.

Solve and check systems of equations using the following methods: graphically, using the substitution method, and using the addition/elimination method.

Create and solve real-world models involving systems of linear equations in two variables.

Properly define variables; include units in variable definitions.

State contextual conclusions using complete sentences.

Given the equations of two lines, classify them as parallel, perpendicular, or neither.