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Big Ideas Math Integrated I, 2016
BI
Big Ideas Math Integrated I, 2016 View details
6. Graphing Linear Inequalities in Two Variables
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Exercise 32 Page 253

How do you determine which half-plane is to be shaded?

Error: The opposite half-plane should be shaded.
Correct Graph:

Practice makes perfect

To graph the given inequality, we will begin by graphing the boundary line, y=3x-2. Note that since the inequality is not strict, the boundary line will be solid.

Let's now use (0,0) as a test point to check whether the shaded half-plane is correct.

y≤ 3x-2
SubstituteII

x= 0, y= 0

0 ? ≤ 3( 0) -2
ZeroPropMult

Zero Property of Multiplication

0 ? ≤ 0 -2
SubTerm

Subtract term

0≰ -2 *

Since the test point did not produce a true statement, we will shade the region that does not contain (0,0).

The error was shading the incorrect half-plane.
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arrow_right Communicate Your Answer p.249
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Communicate Your Answer 5 (Page 249)
arrow_right Monitoring Progress p.250-252
Monitoring Progress 1 (Page 250)
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Monitoring Progress 9 (Page 252)
arrow_right Exercises p.253-254
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