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CHAPTER 3 Graphs of Liner Equations Slide 2Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. 3.1Graphs and Applications of Linear Equations 3.2More with Graphing and Intercepts 3.3Slope and Applications 3.4Equations of Lines 3.5Graphing Using the Slope and the y-Intercept 3.6Parallel and Perpendicular Lines 3.7Graphing Inequalities in Two Variables

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OBJECTIVES 3.7 Graphing Inequalities in Two Variables Slide 3Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. aDetermine whether an ordered pair of numbers is a solution of an inequality in two variables. bGraph linear inequalities.

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The solutions of inequalities in two variables are ordered pairs. 3.7 Graphing Inequalities in Two Variables a Determine whether an ordered pair of numbers is a solution of an inequality in two variables. Slide 4Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE We use alphabetical order to replace x with 1 and y with 3. 3x + 4y < 15 3(1) + 4(2) ? 15 3 + 8 11 True Since 11 < 15 is true, (1, 2) is a solution. 3.7 Graphing Inequalities in Two Variables a Determine whether an ordered pair of numbers is a solution of an inequality in two variables. ADetermine whether (1, 2) is a solution of 3x + 4y < 15. Slide 5Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE Solution: We first graph the line y = 2x. Every solution of y = 2x is an ordered pair like (1, 2). Draw the line dashed because its points are not solutions. 3.7 Graphing Inequalities in Two Variables b Graph linear inequalities. BGraph y < 2x (continued) Slide 6Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE Solution: Select a point on one side of the half-plane and check in the inequality. Try (2, 0) y < 2x 0 < 2(2) 0 < 4 TRUE Shade the half-plane containing the point. 3.7 Graphing Inequalities in Two Variables b Graph linear inequalities. BGraph y < 2x (continued) Slide 7Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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1. Replace the inequality symbol with an equals sign and graph this related equation. 2.If the inequality symbol is, draw the line dashed. If the inequality symbol is or , draw the line solid. 3.7 Graphing Inequalities in Two Variables To graph an inequality in two variables: (continued) Slide 8Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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3.The graph consists of a half-plane, either above or below or left or right of the line, and, if the line is solid, the line as well. 4. To determine which half-plane to shade, choose a point not on the line as a test point. Substitute to find whether that point is a solution of the inequality. 3.7 Graphing Inequalities in Two Variables To graph an inequality in two variables: Slide 9Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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5. If it is, shade the half-plane containing the point. If it is not, shade the half-plane on the opposite side of the line. 3.7 Graphing Inequalities in Two Variables To graph an inequality in two variables: Slide 10Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE 1. First, we graph the line. The intercepts are (0, –3) and (6, 0). 2. Since the inequality contains the ≤ symbol, we draw the line solid to indicate that any pair on the line is a solution. 3.7 Graphing Inequalities in Two Variables b Graph linear inequalities. CGraph: x – 2y ≤ 6 (continued) Slide 11Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE Shade the half-plane containing the point. 3. Next, we choose a test point. (0, 0) x – 2y ≤ 6 0 – 2(0) ≤ 6 0 ≤ 6 TRUE 3.7 Graphing Inequalities in Two Variables b Graph linear inequalities. CGraph: x – 2y – 6 Slide 12Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE 1. Graph the line x = 1. 2. Since the inequality symbol is >, use a dashed line. 3. Choose a test point. (0, 0) x + 0y > 1 0 – 0(0) > 1 0 > 1 FALSE 3.7 Graphing Inequalities in Two Variables b Graph linear inequalities. DGraph x > 1 (continued) Slide 13Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE Shade on the other half-plane. The solutions are all ordered pairs with first coordinates > 1. 3.7 Graphing Inequalities in Two Variables b Graph linear inequalities. DGraph x > 1 Slide 14Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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A linear inequality is similar to a linear equation, but the equal sign is replaced with an inequality symbol. A solution of a linear inequality is any.

A linear inequality is similar to a linear equation, but the equal sign is replaced with an inequality symbol. A solution of a linear inequality is any.

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