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Graphing Linear Inequalities in Two Variables

Learn to graph linear inequalities in two variables step by step, including how to graph the boundary line, test points, and shade the correct regions. Practice examples provided. Homework exercises included.

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Graphing Linear Inequalities in Two Variables

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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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