1. 2.8 Graphing Linear and Absolute Value Inequalities
by Johnathan Wu

2. Vocabulary
Linear inequality- a linear equation, but with an inequality sign instead of an equal sign
Boundary- a line that separate the coordinate plane into regions
Absolute Value inequality- an absolute value equation, but with an inequality sign instead of an equal sign

3. Example Problem: Graphing Linear inequalities
Graph the inequality: 2x - 3y≥6
Rewrite the equation in y-intercept form: y = mx + b. Where m represents the slope and b represents the y- intercept.
2x – 3y ≥ 6 ⇒ y ≤ x – 2
Then graph.
If the inequality is ≤ or ≥ then we draw a solid line. If the inequality is < or > then we draw a dotted line.
When graphing inequalities,
y > or y ≥ means shade UP
y < or y ≤ mean shade DOWN

4. Example problem: Absolute Value Inequalities
Graph the inequality: y ≥ lxl
Graph the absolute value inequality as a absolute value equation
The y-intercept is 0 and the slope is 1
Since the symbol is a ≥, it is a solid line and you shade up

5. Practice problems Linear inequalities: Absolute Value Inequalities:
y≥x - 5
Absolute Value Inequalities:
y ≥ lxl + 1

6. ANSWERS
y ≥ lxl + 1
y≥x - 5