In this lesson… We will write and graph linear inequalities.

In this lesson…

We will write and graph linear inequalities

Sharon earns $8 an hour and a bonus of $24 each week.

Write an equation describing Sharon’s

weekly pay.

Complete the table:

Hours Process Total Pay

0

1

2

3

x y

Complete the table:

Hours Process Total Pay

0 8(0) + 24 24

1 8(1) + 24 32

2 8(2) + 24 40

3 8(3) + 24 48

x 8x + 24 y

An equation to describe the total weekly earnings in terms of the number of

hours worked is…

y = 8x + 24

The amount Sharon needs to pay all of her bills must be less than

or equal to the amount she earns

An inequality to describe the amount Sharon needs

to earn to pay her bills is …

8 24y x

Graph this Inequality

Begin at the y-intercept

8 24y x

hours

Bills ($)

8

1 2 3 4 5

16243240

Find a 2nd point with the slope

8 24y x

hours

Bills ($)

8

1 2 3 4 5

16243240

Connect the points with a line

8 24y x

hours

Bills ($)

8

1 2 3 4 5

16243240

Shade below the line

hours

8 24y x

hours

Bills ($)

8

1 2 3 4 5

16243240

The shaded region

represents the the

amounts Sharon

can afford

Paul claims he can run 4 miles a day. He has already

run 32 miles this month.

An equation describing the total number of miles that

Paul has run in terms of the days is y = 4x + 32

Paul’s coach insists he run more than 4 miles each day to prepare

to run in a marathon.

Write an inequality describing the total miles the

coach wants Paul to run.

The inequality shows the total miles,

y, is greater than 4x + 32

y > 4x + 32

Graph this inequality

First Graph the y-intercept

4 32y x

days

Total Miles

4

1 2 3 4 5

812162432

3640

Graph a second point

4 32y x

days

Total Miles

4

1 2 3 4 5

812162432

3640

Connect with a dotted line4 32y x

days

Total Miles

4

1 2 3 4 5

812162432

3640

The points on the line are not included since Paul must jog MORE than the amounts on the line

Shade ABOVE the line4 32y x

days

Total Miles

4

1 2 3 4 5

812162432

3640

The shaded region

represents the miles

Paul must run

The Student Council is purchasing T-shirts and

Posters to sell for a school fundraiser

Each T-Shirt costs $6 and each poster costs $2

The Student Council Sponsor says that they

must keep their spending below $120 for this

fundraiser

If T is the number of T-shirts, then 6T is the cost for all the T-Shirts

If P is the number of posters, then 2P is the cost for all the posters

Since they must spend less than $120, the inequality

for this problem is…

6T + 2P < 120

To graph this inequality, we can use T and P

intercepts

6T + 2P < 120

T P0

0

To graph this inequality, we can use T and P

intercepts

6T + 2P < 120

T P20 0

0 60

Graph each ordered pair

Posters

10

5 10 15 20 25

20

30

40

50T P20 0

0 60

T-Shirts

60

6T + 2P < 120

Connect with a dotted line

Posters

10

5 10 15 20 25

20

30

40

50T P20 0

0 60

T-Shirts

60

6T + 2P < 120

Shade below the line

Posters

10

5 10 15 20 25

20

30

40

50T P20 0

0 60

T-Shirts

60

6T + 2P < 120

The shaded region represents the numbers of T-Shirts and Posters the

Student Council can affordPosters

10

5 10 15 20 25

20

30

40

50

T-Shirts

60 Can they afford 15 T-Shirts and 30

posters?

Can they afford 15 T-Shirts and 30

posters?

Complete Activity 6d

Write Linear Inequalities

Graph Linear Inequalities

Solve Problems using Linear Inequalities