AlgebraStructure & Method · Book 1All Chapters

Inequalities in Two Variables

10-7Graphing Linear Inequalities

Overview

Graph y = mx + b. Shade above for y > … and below for y < …. Dashed line for strict (<, >); solid for ≤, ≥.

Key ideas

  • Draw boundary first.
  • Pick a test point (often (0, 0)).
  • Shade the side that satisfies the inequality.

Worked examples

Example 1

Problem. Graph y > x − 1.

Solution. Dashed line y = x − 1; shade above.

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Solid or dashed for y ≤ 2x?

  2. 2.

    Shade above or below for y < −x + 3?

  3. 3.

    Test point (0,0) in y ≥ x + 2: satisfy?

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    Graph the inequality: y > 2x − 1.

  2. 2.

    Graph the inequality: 3x + 2y ≤ 6.