Graph a two-variable linear inequality

Graph inequality solution regions using boundary lines and shading.

Do this: Read the concept below, then try the quiz or activity.

Lesson 75 of 192
39%

Concept

Objective: Students will graph and interpret solution regions of linear inequalities.

Estimated Time: 12 minutes

Standards:
HSA-REI.D.10HSF-IF.C.7

Graph the boundary line first. Use dashed lines for < or > and solid lines for ≤ or ≥, then shade the correct side.

Try it

Graph y ≥ -x + 2 and identify whether (0,0) is in the solution set.

📈 Coordinate Grapher

Use inequality mode and verify your shading decision with test points.

y = y = 1x
-10-9-8-7-6-5-4-3-2-112345678910-10-9-8-7-6-5-4-3-2-112345678910

Concept Check

For y < 3x - 1, the boundary line is:

Concept Check

Why test a point after drawing the boundary?

Common Misconception
Always verify your result in context instead of trusting a first pass.

Graph inequality steps

These steps are out of order — can you fix them?

1.Shade true region
2.Graph boundary line style
3.Rewrite in slope-intercept form
4.Test a point

Short Answer

How do line style and shading encode the solution set?

Mastery Check

Pass this check with at least 80% to unlock completion.

Question 1

For y < 3x - 1, the boundary line is:

Question 2

Why test a point after drawing the boundary?

Pass the mastery check (80%+) to unlock completion.