Graphing inequalities

Math

Definition

The process of representing inequalities on a number line or coordinate plane. On a number line, open circles show < or > and closed circles show ≤ or ≥. On a coordinate plane, dashed lines show strict inequalities and solid lines show inclusive ones, with shading on the solution side.

How It Works

  1. Graph the boundary line or point (dashed for < or >, solid for ≤ or ≥).
  2. Choose a test point not on the boundary (often the origin).
  3. Substitute the test point into the inequality.
  4. If the test point satisfies the inequality, shade that side; otherwise shade the opposite side.

Examples

  • y > 2x + 1 is graphed with a dashed line and shading above
  • x ≤ 3 on a number line has a closed dot at 3 with shading to the left
  • y ≤ −x + 4 uses a solid line with shading below

Related Terms

Solving inequalities Compound inequalities Writing inequalities Slope-intercept form

Study This Concept

Practice graphing inequalities with free review games in these units:

Pre-Algebra Unit 7: Inequalities