2.8 Graphing Linear and Absolute Value Inequalities by Johnathan Wu

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

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

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

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

ANSWERS y ≥ lxl + 1 y≥x - 5