Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall

Chapter 3 Graphs and Functions

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall 3.7 Graphing Linear Inequalities

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Linear Inequalities in Two Variables Linear Inequality in Two Variables Written in the form Ax + By < C A, B, C are real numbers, A & B are not both 0 Could use (>, ,  ) in place of < An ordered pair is a solution of the linear inequality if it makes the inequality a true statement.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall

Graph 7x + y > –14. Solution x y Pick a point not on the graph: (0,0) Graph 7x + y = –14 as a dashed line. Test it in the original inequality. 7(0) + 0 > –14, 0 > –14 True, so shade the side containing (0,0). (0, 0) Example 1

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Graph 3x + 5y  –2. Solution x y Pick a point not on the graph: (0,0), but just barely Graph 3x + 5y = –2 as a solid line. Test it in the original inequality. 3(0) + 5(0) > – 2, 0 > – 2 False, so shade the side that does not contain (0,0). (0, 0) Example

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Graph 3x < 15. Solution x y Pick a point not on the graph: (0,0) Graph 3x = 15 as a dashed line. Test it in the original inequality. 3(0) < 15, 0 < 15 True, so shade the side containing (0,0). (0, 0) Example

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Graph the intersection of x  1 and y  2x – 1. Example 3 Solution Graph each inequality. The intersection of the two graphs is all points common in both regions.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Graph the union of Example 4 Solution Graph each inequality. The union of both inequalities is both shaded regions, including the solid boundary line shown in the third graph.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall 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. Warning!