Graphs

Graphs are found in all areas of our lives — from commercials showing which cell phone carrier provides the best coverage, to bank statements and news articles, to the boardroom of major corporations. This chapter studies the rectangular coordinate system, which is the basis for most consumer graphs. We will look at linear graphs, slopes of lines, equations of lines, and linear inequalities.

Sections

• Use the Rectangular Coordinate System — plotting points in the $xy$-plane, verifying solutions to an equation in two variables, completing a table of solutions, and finding solutions to a linear equation in two variables.
• Graph Linear Equations in Two Variables — graphing by plotting points, graphing vertical and horizontal lines, and graphing using a table of solutions.
• Graph with Intercepts — identifying the $x$- and $y$-intercepts of a line, graphing a line using its intercepts, and choosing the most convenient method to graph a line.
• Understand Slope of a Line — finding the slope of a line from its graph, from two points, and using the slope formula; graphing a line given a point and the slope.
• Use the Slope-Intercept Form of an Equation of a Line — recognizing slope and $y$-intercept from an equation, graphing with the slope-intercept form, and identifying parallel and perpendicular lines.
• Find the Equation of a Line — finding an equation given the slope and a point, given two points, or given a point and a parallel or perpendicular line.
• Graphs of Linear Inequalities — verifying solutions to a linear inequality in two variables and graphing linear inequalities in two variables.

This chapter overview is adapted from Elementary Algebra 2e, Chapter 4 Introduction by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, © OpenStax, licensed under CC BY-NC-SA 4.0. Access the original for free at openstax.org. Changes: condensed the chapter introduction and recast the chapter outline as a section list.