McGraw-Hill Ryerson
Pre-Calculus 11
Chapter 9
Linear and Quadratic Inequalities
Section 9.1
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Chapter
9
Linear Inequalities
The graph of the linear equation x – y = –2 is referred to as a boundary
line. This line divides the Cartesian plane into two regions:
For one region, the condition x – y < –2 is true.
For the other region, the condition x – y > –2 is true.
Use the pen to label the conditions
below to the corresponding parts of
the graph on the Cartesian plane.
x – y < –2
x – y = –2
x – y < –2
x – y > –2
x – y > –2
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Linear Inequalities
Chapter
9
The ordered pair (x, y) is a solution to a linear inequality if its coordinates
satisfy the condition expressed by the inequality.
Which of the following ordered pairs (x, y)
are solutions of the linear inequality
x – 4y < 4?
Click on the ordered pairs to check your
answer.
3

2,


2 

 3 
  2 ,2 


3


2,


2 

0,0
 0,4 
0, 4 
 4,0 
 4,0
x  4y  4
Use the pen tool to graph the boundary line
and plot the points on the graph. Then,
shade the region that represents the
inequality.
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Click here for the solution.
Chapter
9
Graphing Linear Inequalities
Match the inequality to the appropriate graph of a boundary line below.
Complete the graph of each inequality by shading the correct solution region.
Match
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Shade
Graphing a Linear Inequality
Chapter
9
Use the pen tool to graph the following inequalities. Describe the steps
required to graph the inequality.
a)
Click here for the solution.
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Chapter
9
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Graphing a Linear Inequality
Match each inequality to its graph.
Then, click on the graph to check the answer.
Linear Inequalities
Chapter
9
Write an inequality that represents each graph.
2.
1.
(2, 4)
(0, 3)
0
0
(2, -1)
2x  y  3
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(0, -2)
3x  y  2
Chapter
Solve an Inequality
9
Paul is hosting a barbecue and has decided to budget $48 to purchase
meat. Hamburger costs $5 per kilogram and chicken costs $6.50 per
kilogram.
Write an inequality to represent the number of
Let h = kg of hamburger
kilograms of each that Paul may purchase.
c = kg of chicken
Chicken
Write the equation of the boundary line
below and draw its graph.
Shade the solution region for the inequality.
Hamburger
Click here for the solution.
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Solve an Inequality
Chapter
c
9
Chicken
5h  6.5c  48
h
Hamburger
1. Can Paul buy 6 kg of hamburger and 4 kg chicken if he wants to stay within his set
budget?
No
2. How many kilograms of chicken can Paul buy if he decides not to buy any hamburger?
7.38 kg
3. If Paul buys 3 kg of hamburger, what is the greatest number of kilograms of chicken he
can buy?
5.08 kg
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Click here for the solution.
For next class complete
the following:
p. 472, #1 a, #2a, #3 c, e,
#4 a, b, # 9,
p. 473, #17
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The following pages contain solutions for the
previous questions.
Click here to return to the start
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Solutions
(0, 4)
0
(-4, 0)
(0, 0)
(4, 0)
(0, -4)
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Go back to the question.
Solutions
An example method for graphing an inequality would be:
1
• Slope of the line is 3 .
and the y-intercept is the point (0, 1).
• The inequality is less than. Therefore,
the boundary line is a broken line.
• Use a test point (0, 0). The point
makes the inequality true.
• Therefore, shade below the line.
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• The x-intercept is the point (–2, 0), the
y-intercept is the point (0, –4).
• The inequality is greater than and equal to.
Therefore, the boundary line is a solid line.
• Use a test point (0, 0). The point makes
the inequality true.
• Therefore, shade above the line.
Go back to the question.
Solutions
Let h = kg of hamburger
c = kg of chicken
Write an inequality to represent the number of
kilograms of each that Paul may purchase.
c
Chicken
Graph the boundary line for the inequality.
h
Hamburger
Go back to the question.
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Solutions
c
5h  6.5c  48
Chicken
(0, 7.38)
(3, 5)
(6, 4)
h
Hamburger
1. Can Paul buy 6 kg of hamburger and 4 kg chicken if he wants to stay within his set budget?
The point (6, 4) is not within the shaded region. Paul could
not purchase 6 kg of hamburger and 4 kg of chicken.
2. How many kilograms of chicken can Paul buy if he decides not to buy any hamburger?
This is the point (0, 7.38). Buying no hamburger would be
the y-intercept of the graph.
3. If Paul buys 3 kg of hamburger, what is the greatest whole number of kilograms of chicken he can
buy?
This would be the point (3, 5). Paul could buy 5 kg of
chicken.
Pen Tool
Go back to the question.