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Chapter 7 Section 5 Graphing Linear Inequalities

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Learning Objective Graph a linear inequalities in two variables. Key Vocabulary: linear inequalities in two variables coordinate plane region

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Graphing Linear Inequalities Linear inequalities is when you replace the equal sign with an inequality sign. > < ≤ ≥ There are two regions: one above the equation line one below the equation line 2 1 y x Equation

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Graphing Linear Inequalities Examples: For each inequality, determine if the boundary line for the graph will be dashed or solid. a)3x < 4y dashed line b)2x + 3y ≥ 72solid line c)-3x – 4y ≤ 13solid line d)-5x + 11y > 41 dashed line

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Graphing Linear Inequalities EXAMPLES: Determine if the ordered pair (3, -2) is a solution to the inequality a) 4x – 3y > 3b)-2x + 5y ≤ 0 4(3) – 3(-2) > 3-2(3) + 5(-2) ≤ 0 12 + 6 > 3-6 – 10 ≤ 0 18 > 3-16 ≤ 0True c)4x + 7y ≥ 2d)8x + 3y < -5 4(3) + 7(-2) ≥ 28(3) + 3(-2) < -5 12 – 14 ≥ 2 e) 3x + 9y ≤ -924 – 6 < -5 -2 ≥ 2 3(3) + 9(-2) ≤ -918 < -5 False 9 – 18 ≤ -9False -9 ≤ -9 True

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Graphing Linear Inequalities Graph Replace inequality with an equal sign Solve for y and choose at least three values for x this will give you three sets of ordered pairs Draw the graph of the equation ≤ or ≥ draw a solid line > or < draw a dotted line Select any point not on the line and determine if it is a solution. A good point to choose if not on the line is (0, 0) If true shade that region If false shade the opposite region

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Graphing Linear Inequalities EXP: Graph the inequality y < x – 1 change inequality to equal sign y = x – 1 m = 1 y-intercept (0, -1) Positive slope up 1 right 1 (0,0) (0,-1) (2,1) (1,0) xy 0 10 21 y < x – 1 point (0, 0) 0 < 0 – 1 0 < -1 FALSE Two way to graph 1.Slope Intercept 2.Plotting the points

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Graphing Linear Inequalities EXP: Graph the inequality y ≥ - ⅓ x change inequality to equal sign y = - ⅓ x m = ⅓ y-intercept (0,0) Negative slope down 1 right 3 (3,-1) (6,-2) xy 00 3 6-2 y ≥ -⅓ (x) point (3,1) 1 ≥ -⅓ (3) 1 ≥ -1 TRUE (0,0) (3,1) Two way to graph 1. Slope Intercept 2. Plotting the points

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Graphing Linear Inequalities EXP: Graph the inequality 3x – y > 6 change inequality to equal sign m = 3 y-intercept (0, -6) Positive slope up 3 right 1 (0,-6) (2,0) xy 0-6 1-3 20 3x – y > 6 point (0,0) 3(0) – 0 > 6 0 > 6 FALSE (0,0) (1,-3) Two way to graph 1. Slope Intercept 2. Plotting the points

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Graphing Linear Inequalities EXP: Graph the inequality y ≤ 5 change inequality to equal sign Horizontal line m = 0 (2,5) (0,0) (-2.5) y ≤ 5 point (0,0) 0 ≤ 5 TRUE

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Graphing Linear Inequalities EXP: Graph the inequality x > -3 change inequality to equal sign Vertical line Slope is undefined x > -3 point (0,0) 0 > -3 True (-3,2) (0,0) (-3,-2)

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Remember > and < are strict inequalities and are dashed lines on the graph ≤ and ≥ are non-strict inequalities and are solid lines on the graph Change the inequality to and equal sign Solve for y Use the slope and y-intercept or use plotting points to graph the equation Select a test point not on the line true shade that region false shade the opposite region

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HOMEWORK 7.5 Page 468: #5, 7, 9, 11, 13, 19, 21, 23

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