Graphing Linear Functions
Lessons in this chapter
About Graphing Linear Functions
Graphing Linear Functions applies the function vocabulary from earlier in the course specifically to linear equations.
Linear Functions frames y = mx + b as a function rule, before Graphing Linear Equations in Standard Form and Graphing Linear Equations in Slope-Intercept Form cover the two most common equation forms and their own quick graphing methods.
Transformations of Graphs of Linear Functions applies the translation, reflection, and scaling ideas from Functions: Transformations specifically to lines, while Graphing Absolute Value Functions builds the distinctive V-shaped graph of y = |x| and its transformations.
All five lessons here open as Algebra 1 worksheets in the page, including Graphing Linear Equations in Slope-Intercept Form, Transformations of Graphs of Linear Functions and Graphing Absolute Value Functions. Each question is scored as it is answered, so a slope read as rise over run in the wrong order is caught on the first graph rather than the tenth. The practice is free to try, with no login needed for your first 3.
Frequently asked questions
Linear Functions opens by identifying what makes a function linear, then Graphing Linear Equations in Standard Form plots a line from its intercepts and Graphing Linear Equations in Slope-Intercept Form plots it from a starting point and a slope. Transformations of Graphs of Linear Functions shifts, reflects and stretches those lines, and Graphing Absolute Value Functions introduces the V-shaped graph that the same transformations apply to. The chapter draws on the high school Algebra (A) and Functions (F) conceptual categories.
Slope-intercept form (y = mx + b) shows the slope and y-intercept directly; standard form (Ax + By = C) is often faster for finding both the x- and y-intercepts by setting the other variable to zero.
Plot the y-intercept first, then use the slope (rise over run) to find a second point, and draw a line through both points.
Find the x-intercept (set y = 0 and solve for x) and the y-intercept (set x = 0 and solve for y), plot both points, and draw a line through them.
The same vertical shift, horizontal shift, reflection, and scaling rules from Functions: Transformations apply directly, for instance, y = mx + b + 3 shifts the line up 3 units from y = mx + b.
An absolute value function’s graph is a V-shape, since it reflects the negative half of a linear function up to match the positive half: the vertex of the V is where the expression inside the absolute value equals zero.