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Section 6-7

Section 6-7. Objective: Students will graph inequalities. Graph Linear Inequalities in Two Variables. 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

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Section 6-7

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

  2. 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!

  3. 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

  4. 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.

  5. Example 3 1 Graph the inequality - x + 4y > -8. +1x+1x 4y > 1x – 8 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).

  6. 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).

  7. 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).

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

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