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McGraw-Hill Ryerson

Pre-Calculus 11

Chapter 9

Linear and Quadratic Inequalities

Section 9.1

Click here to begin the lesson

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Linear InequalitiesThe 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.

Chapter

9

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

Click here for the solution.

The ordered pair (x, y) is a solution to a linear inequality if its coordinates

satisfy the condition expressed by the inequality.

Chapter

9Which 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.

Use the pen tool to graph the boundary line

and plot the points on the graph. Then,

shade the region that represents the

inequality.

32,

2

32,

2

3,2

2

0,0

0,4 0, 4

4,0 4,04 4x y

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Graphing Linear InequalitiesChapter

9Match the inequality to the appropriate graph of a boundary line below.

Complete the graph of each inequality by shading the correct solution region.

Match Shade

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Click here for the solution.

Chapter

9a)

Graphing a Linear InequalityUse the pen tool to graph the following inequalities. Describe the steps

required to graph the inequality.

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Chapter

9 Match each inequality to its graph.

Then, click on the graph to check the answer.

Graphing a Linear Inequality

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Linear InequalitiesWrite an inequality that represents each graph.

Chapter

91. 2.

(2, 4)

(0, -2)

0

(0, 3)

(2, -1)

0

3 2x y x y 2 3

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Solve an Inequality

Click here for the solution.

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.

Chapter

9

Let h = kg of hamburger

c = kg of chicken

Write an inequality to represent the number of

kilograms of each that Paul may purchase.

Write the equation of the boundary line

below and draw its graph.

Shade the solution region for the inequality.

Ch

icken

Hamburger

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Click here for the solution.

Chapter

9

1. Can Paul buy 6 kg of hamburger and 4 kg chicken if he wants to stay within his set

budget?

2. How many kilograms of chicken can Paul buy if he decides not to buy any hamburger?

3. If Paul buys 3 kg of hamburger, what is the greatest number of kilograms of chicken he

can buy?

Solve an Inequality

Hamburger

Ch

icke

n

h

c

5 6.5 48h c

No

7.38 kg

5.08 kg

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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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(0, 0)(-4, 0)

(0, 4)

(4, 0)

(0, -4)

Solutions

Go back to the question.

0

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Solutions

• Slope of the line is .

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.

• 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.

An example method for graphing an inequality would be:

Go back to the question.

1

3

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Let h = kg of hamburger

c = kg of chicken

Write an inequality to represent the number of

kilograms of each that Paul may purchase.

Graph the boundary line for the inequality.

Hamburger

Solutions

Go back to the question.

Ch

icke

n

c

h

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1. Can Paul buy 6 kg of hamburger and 4 kg chicken if he wants to stay within his set budget?

2. How many kilograms of chicken can Paul buy if he decides not to buy any hamburger?

3. If Paul buys 3 kg of hamburger, what is the greatest whole number of kilograms of chicken he can

buy?

Hamburger

Ch

icke

n (3, 5)

(6, 4)

(0, 7.38)

The point (6, 4) is not within the shaded region. Paul could

not purchase 6 kg of hamburger and 4 kg of chicken.

This is the point (0, 7.38). Buying no hamburger would be

the y-intercept of the graph.

This would be the point (3, 5). Paul could buy 5 kg of

chicken.

Solutions

Go back to the question.

h

c

5 6.5 48h c