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11.6 graphing linear inequalities in two variables
1.
Slide - 1Copyright
© 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G 2 Graphs of Linear Equations and Inequalities in Two Variables 11
2.
Slide - 2Copyright
© 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G 1. Graph linear inequalities in two variables. 2. Graph an inequality with boundary through the origin. Objectives 11.6 Graphing Linear Inequalities in Two Variables
3.
Slide - 3Copyright
© 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G The inequality 2x + 3y ≤ 6 means that 2x + 3y < 6 or 2x + 3y = 6. The graph of 2x + 3y = 6 is a line. This boundary line divides the plane into two regions. The graph of the solutions of the inequality 2x + 3y < 6 will include only one of these regions. We find the required region by checking a test point. We choose any point not on the boundary line. Because (0, 0) is easy to substitute, we often use it. Graph Linear Inequalities Example Graph the inequality 2x + 3y 6.
4.
Slide - 4Copyright
© 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Graph Linear Inequalities 2x + 3y ≤ 6 2(0) + 3(0) ≤ 6 0 ≤ 6 True. 0 + 0 ≤ 6 Example (cont) Graph the inequality 2x + 3y 6. Check (0, 0) Since the last statement is true, we shade the region that includes the test point (0, 0).
5.
Slide - 5Copyright
© 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Graphing Linear Inequalities Graphing a Linear Inequality Step 1 Graph the boundary. Graph the line that is the boundary of the region. Draw a solid line if the inequality has ≤ or ≥; draw a dashed line if the inequality has < or >. Step 2 Shade the appropriate side. Use any point not on the line as a test point. Substitute for x and y in the inequality. If a true statement results, shade the side containing the test point. If a false statement results, shade the other side.
6.
Slide - 6Copyright
© 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Example Graph the inequality 2x + y > 3. Start by graphing the equation 2x + y = 3. Graphing Linear Inequalities 2x + y = 3 –2x –2x y = –2x + 3 Use a dashed line to show that the points on the line are not solutions of the inequality. -5 -3 -1 -4 -2 1 3 5 2 4 42-2-4 531-1-3-5
7.
Slide - 7Copyright
© 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Example (cont) Graph the inequality 2x + y > 3. Choose any test point not on the line. Here, we choose (0,0) Graph Linear Inequalities 2(0) + (0) > 3 0 > 3 Because 0 > 3 is false, shade the region not containing (0, 0). False -5 -3 -1 -4 -2 1 3 5 2 4 42-2-4 531-1-3-5
8.
Slide - 8Copyright
© 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Example Graph the inequality y < 3x. Begin by graphing y = 3x, using a dashed line. Graph an Inequality with Boundary Through the Origin -5 -3 -1 -4 -2 1 3 5 2 4 42-2-4 531-1-3-5 Since (0, 0) is on the boundary line, choose a different test point. Here, we choose (1,1). 1 < 3(1) 1 < 3 True Thus, we shade the region containing (1,1).
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