8.F.A.3 8th Grade Functions

Graphing Linear Equations

Interpret the equation y = mx + b as defining a linear function whose graph is a straight line, and recognize functions that are not linear.

How to explain it

The anchor students hold onto: y = mx + b · m = slope (rise over run) · b = y-intercept · rewrite Ax + By = C as y = mx + b before graphing.

Use the graph of y = mx + b to compare functions (8.F.A.2), write linear models from data (8.F.B.4), and solve systems visually (8.EE.C.8a).

Worked examples

Example 1 Graph y = 2x − 3

Graph y = 2x − 3.

Step 1Identify: m = 2, b = −3.

Step 2Plot the y-intercept (0, −3).

Step 3Rise 2, run 1: next point (1, −1).

Step 4Draw a line through both points.

AnswerSlope 2; y-intercept (0, −3).

Example 2 Graph 2x + y = 4

Graph 2x + y = 4.

Step 1Rewrite: y = −2x + 4.

Step 2Identify: m = −2, b = 4.

Step 3Plot (0, 4); rise −2, run 1 → (1, 2).

Step 4Draw the line through both points.

AnswerSlope −2; y-intercept (0, 4).

Example 3 Graph y = −2

Graph y = −2.

Step 1Recognize: m = 0 (horizontal line).

Step 2Every point has y-coordinate −2.

Step 3Plot (0, −2) and (3, −2).

Step 4Draw a horizontal line at y = −2.

AnswerSlope 0; every point has y = −2.

Common mistakes

What students write Applying rise and run in the wrong order — running first and then rising.

The fix Always start at the y-intercept. Apply slope as rise first (up or down), then run (right).

Try this A student was asked to graph y = 3x - 2. She plotted the y-intercept at (0, -2) correctly. To find her next point, she moved 1 unit up and 3 units right, reaching (3, -1). Identify the error and describe the correct process.

What students write Starting the graph at the x-intercept instead of the y-intercept.

The fix The b in y = mx + b is the y-intercept. Begin at (0, b) on the y-axis, not where the line hits x.

Teacher tip

Head off the two predictable errors before they happen. First: Always start at the y-intercept. Apply slope as rise first (up or down), then run (right). Second: The b in y = mx + b is the y-intercept. Begin at (0, b) on the y-axis, not where the line hits x.