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6.8
Linear Inequalities in
Two Variables
Copyright © 2009 Pearson Education, Inc.
Slide 6 - 1
To Graph Inequalities in Two Variables
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Mentally substitute the equal sign for the
inequality sign and plot points as if you were
graphing the equation.
If the inequality is < or >, draw a dashed line
through the points. If the inequality is  or ,
draw a solid line through the points.
Select a test point not on the line and substitute
the x and y-coordinates into the inequality. If the
substitution results in a true statement, shade
the area on the same side of the line as the test
point. If the test point results in a false
statement, shade the area on the opposite side
of the line as the test point.
Copyright © 2009 Pearson Education, Inc.
Slide 6 - 2
Example: Graph 3x + 4y > 12
Think: 3x + 4y = 12
Draw a dashed line.
Select a test point.
Try (0, 0)
3x + 4y > 12
3(0) + 4(0) > 12
0 + 0 > 12
0 > 12 false
Shade the opposite
half plane.
Copyright © 2009 Pearson Education, Inc.
Slide 6 - 3
Graph y > -3x - 2
Copyright © 2009 Pearson Education, Inc.
Slide 6 - 4
Example: Graph 3x + y  6
Think: 3x + y = –6
Draw a solid line.
Select a test point.
Try (0, 0)
3x + y  6
3(0) + (0)  6
0 + 0  6
0  6 false
Shade the opposite
half plane.
Copyright © 2009 Pearson Education, Inc.
Slide 6 - 5
Graph x – 2y > 4
Copyright © 2009 Pearson Education, Inc.
Slide 6 - 6
Example: Graph y > 2
Think: y = –2
Draw a dashed line.
Select a test point.
Try (0, 0)
0 > 2 true
Shade the half plane
containing (0, 0).
Copyright © 2009 Pearson Education, Inc.
Slide 6 - 7
Graph x > 2 on a coordinate plane
Copyright © 2009 Pearson Education, Inc.
Slide 6 - 8
Homework
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P. 351 # 3 - 28
Ch. 6.6-6.7 quiz next class
Copyright © 2009 Pearson Education, Inc.
Slide 6 - 9