6­6 New Notes (USE THESE).notebook
August 15, 2012
Graphing Inequalities in Two
Variables
6­6
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6­6 New Notes (USE THESE).notebook
August 15, 2012
Review
Solve for y in terms of x
• 3x + 2y = 12
• 6x + 3y = 9
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6­6 New Notes (USE THESE).notebook
August 15, 2012
• Graph y = ¾ x + 2
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6­6 New Notes (USE THESE).notebook
August 15, 2012
Half­ plane
Boundary
Half­ plane
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6­6 New Notes (USE THESE).notebook
August 15, 2012
• Graph: y > 3x + 2
4
• Test the region
Dashed line because y is not also
“equal” to…
Check pts above and below the line for the solution.
Try (0, 0)
Shade in the region for the solutions.
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6­6 New Notes (USE THESE).notebook
August 15, 2012
Graph : y ­2x < ­4 Ex 2
• Solve for y in terms of x
Graph as:
Draw the line.
Test points:
Shade the solution half.
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6­6 New Notes (USE THESE).notebook
August 15, 2012
Example 3
• Graph 2y – 4x > 6
• Solve for y in terms of x
2) Will the line be solid?
3) Graph
4) Test a region for the solution.
5) Shade in the correct region.
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6­6 New Notes (USE THESE).notebook
August 15, 2012
• y > 2 x + 3
Test (0,0)
O > 2(0) + 3
False!
Shade the region to the left
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6­6 New Notes (USE THESE).notebook
August 15, 2012
Example 4
• 3x + 2y < 12
•
•
•
•
•
Solve for y in terms of x
Will the line be solid?
Graph
Test a region
Shade the solution
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6­6 New Notes (USE THESE).notebook
August 15, 2012
Solution y < ­3 + 6
2
check:
Test (0,0)
O < ­3 (0) + 6
2
True!
Shade the region to the left.
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6­6 New Notes (USE THESE).notebook
August 15, 2012
Quick Check
1. Which ordered pair is not a part of the solution set for 4y ­ 2x < 8?
A.(2, 1) B.(3, 2) C.(­3, 5) D.(­4, ­4)
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6­6 New Notes (USE THESE).notebook
August 15, 2012
2. Which is the graph of the inequality y ­ x < 6?
B
A
C
D
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6­6 New Notes (USE THESE).notebook
August 15, 2012
Which of the following is the inequality for the given graph?
A 3x + y > 2
C 3x – y < 2
B 3x + y < 2
D 3x – y > 2
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