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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
