1. Section 2.8 – Graphing Linear Inequalities
EQ: How can I interpret a linear inequality in order to graph?

2. Linear Inequality
resembles a linear equation, but with an inequality instead of an equals symbol. For example,
y > –3x – 2 versus y = –3x – 2.
*The graph of the inequality y > –3x – 2 is shown at the right as a shaded region. *Every point in the shaded region satisfies the inequality. The graph of y = –3x – 2 is the boundary of the region. It is drawn as a dashed line to show that points on the line do not satisfy the inequality. If the symbol was ≤ or ≥, then the points on the boundary would satisfy the inequality, so the boundary would be written as a solid line.

3. Steps to Graphing Linear Inequalities
Write the inequality in slope intercept form.
Graph the inequality
Connect the dots:
With a solid line if ≤ or ≥
With a dashed line is < or >
Shade:
Above the line if > or ≥
Below the line if < or ≤

4. Example 1
Graph x – 2y < 4
Step 1: Put equation in slope – intercept form
−2𝑦<−𝑥+4
𝑦> 1 2 𝑥−2
Step 2: Graph
Step 3: Shade according to inequality
Must flip sign since you are dividing by a negative

5. Example 2
Graph 2x + 5y > 10
5𝑦≥−2𝑥+10
𝑦≥− 2 5 𝑥+2

6. Example 3
Graph x – y > –2
−𝑦>−𝑥−2
𝑦<𝑥+2

7. You Try!
Graph 9x + 3y – 6 ≤ 0
Do on your own!

8. Online Book Access

9. Homework: pg. 119 #8 – 11, 16, 17, 21, 24