8.EE.B.6 8th Grade Expressions & Equations

Slope-Intercept Form

Use similar triangles to explain why the slope is the same between any two distinct points on a line, and derive the equation y = mx + b.

How to explain it

The anchor students hold onto: To graph y = mx + b: plot the y-intercept (0, b) first. From there, use the slope m as rise over run to find a second point. Draw the line through both points.

Students use slope-intercept form to graph and compare linear functions in Graphing Linear Equations, then find intersections in Systems by Graphing.

Worked examples

Example 1 Graph y = 2x + 1

Graph y = 2x + 1.

Step 1Read off the form: m = 2; b = 1.

Step 2Plot the y-intercept (0, 1).

Step 3From (0, 1) rise 2, run 1 → (1, 3).

Step 4Draw a line through both points.

AnswerSlope 2; y-intercept (0, 1).

Example 2 Graph y = −x + 4

Graph y = −x + 4.

Step 1Read off the form: m = −1; b = 4.

Step 2Plot the y-intercept (0, 4).

Step 3From (0, 4) drop 1, run 1 → (1, 3).

Step 4Both lines meet at P(1, 3).

AnswerSlope −1; y-intercept (0, 4).

Common mistakes

What students write Reading the y-intercept off the x-axis — plotting (b, 0) instead of (0, b).

The fix The y-intercept is always on the y-axis where x = 0. Plot (0, b), not (b, 0).

Try this A student graphs y = 3x + 5 by plotting (5, 0) first, then counting up 3 and right 1 to a second point. Their graph is incorrect. Identify the error. Describe the correct first step.

What students write Swapping rise and run — moving horizontally first, then vertically.

The fix Slope = rise ÷ run: vertical change first, horizontal second.

Teacher tip

Head off the two predictable errors before they happen. First: The y-intercept is always on the y-axis where x = 0. Plot (0, b), not (b, 0). Second: Slope = rise ÷ run: vertical change first, horizontal second.