1. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 10 Graphing Equations and Inequalities

2. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 10.7 Graphing Linear Inequalities in Two Variables

3. Martin-Gay, Developmental Mathematics, 2e 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Linear inequality in two variables Written in the form Ax + By < C A, B, C are real numbers, A and B are not both 0 Could use (>, ≥, ≤) in place of < An ordered pair is a solution of the linear inequality in x and y if replacing the variables with the coordinates of the ordered pair results in a true statement. Linear Inequalities in Two Variables

4. Martin-Gay, Developmental Mathematics, 2e 44 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. To Graph a Linear Inequality Step 1: Graph the boundary line found by replacing the inequality sign with an equal sign. If the inequality sign is > or <, graph a dashed boundary line (indicating that the points on the line are not solutions of the inequality). If the inequality sign is ≥ or ≤, graph a solid boundary line (indicating that the points on the line are solution of the inequality). continued Linear Inequalities in Two Variables

5. Martin-Gay, Developmental Mathematics, 2e 55 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Step 2:Choose a point not on the boundary line as a test point. Substitute the coordinates of this test point into the original inequality. Step 3:If a true statement is obtained in Step 2, shade the half-plane that contains the test point. If a false statement is obtained, shade the half-plane that does not contain the test point. Linear Inequalities in Two Variables continued

6. Martin-Gay, Developmental Mathematics, 2e 66 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Graph: 7x + y > –14. x y Step 2: Choose a test point not on the boundary line. We choose (0,0), and substitute the coordinates into 7x + y > –14. Step 1: First graph the boundary line 7x + y = –14 as a dashed line because the inequality symbol is >. 7(0) + 0 > –14 True Step 3: Since the result is a true statement, (0, 0) is a solution of 7x + y > –14, so shade the side containing (0,0). (0, 0) Example

7. Martin-Gay, Developmental Mathematics, 2e 77 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Graph: 3x + 5y ≤ –2. Example Step 2: Choose a test point not on the boundary line. We choose (0,0), and substitute the coordinates into 3x + 5y ≤ –2. Step 1: First graph the boundary line 3x + 5y ≤ –2 as a solid line because the inequality is ≤. 3(0) + 5(0) ≤ –2 False Step 3: Since the result is a false statement, shade the side that doesn’t contain (0,0).

8. Martin-Gay, Developmental Mathematics, 2e 88 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Graph 3x < 15. x y (0, 0) Example Step 2: Choose a test point not on the boundary line. We choose (0,0), and substitute the coordinates into 3x < 15. Step 1: First graph the boundary line 3x < 15 as a dashed line. 3(0) < 15 True Step 3: Since the result is a true statement, shade the side that contains (0,0).

9. Martin-Gay, Developmental Mathematics, 2e 99 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Helpful Hint When graphing an inequality, make sure the test point is substituted into the original inequality. Also, note that although all of our examples allowed us to select (0, 0) as our test point, that will not always be true. If the boundary line contains (0,0), you must select another point that is not contained on the line as your test point.