Graph Linear Inequalities in Two Variables Section 6-7 Graph Linear Inequalities in Two Variables Objective: Students will graph inequalities Standard: A.REI.12 , F.L.E.5

Graphing a Linear Inequality in Two Variables Step 1: Graph the boundary line. ●Use a dashed line for < or > and ●Use a solid line for ≤ or ≥ Step 2: Test a point not on the boundary line by checking whether the ordered pair is a solution of the inequality. ● Always use (0,0) if the line DOES NOT go through the origin. Step 3: ● If it IS a solution: SHADE TOWARD the POINT! ● If it IS NOT a solution: SHADE AWAY FROM the POINT!

Example 1 Is the point solution of x + 2y ≥ 7?: a) (-1,4) x y • Substitute -1 for x and 4 for y. (-1) + 2(4) ≥ 7 • Simplify. -1 + 8 ≥ 7 • 7 is ≥ 7, so YES (-1, 4) is a solution to the inequality. 7 ≥ 7

Example 2 Graph the inequality y ≥ 3x + 1. •Step 1: Graph • Step 2: Pick a Test point (0, 0) and substitute into the inequality: y ≥ 3x + 1 0 ≥ 3(0) + 1 0 ≥ 1 0 ≥ 1 is False, so you shade AWAY.

Example 3 Graph the inequality - x + 4y > -8. 1 +1x +1x 4 4 4 Step 1: Put inequality in slope-intercept form. •Step 2: Graph • Step 3: Pick a Test point (0, 0) and substitute into the inequality: y > ¼ x - 2 -x + 4y > -8 -(0) + 4(0) > -8 0 > -8 0 > -8 is True, so you shade toward the point (0, 0).

Example 4 Graph the inequality y < 1. •Step 1: Graph • Step 2: Pick a Test point (0, 0) and substitute into the inequality. y < 1 0 < 1 0 < 1 is True, so you shade over the point (0, 0).

Example 5 Graph the inequality x ≥ 2. •Step 1: Graph • Step 2: Pick a Test point (0, 0) and substitute into the inequality. x ≥ 2 0 ≥ 2 0 ≥ 2 is False, so shade away from (0, 0).

Homework Section 6-7 Pg. 409 – 412 4 – 14 even, 15 17, 20, 21, 23, 24, 26, 29, 30, 40 – 41 (no graphing) 53,