in this lesson… we will write and graph linear inequalities
TRANSCRIPT
![Page 1: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/1.jpg)
In this lesson…
We will write and graph linear inequalities
![Page 2: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/2.jpg)
Sharon earns $8 an hour and a bonus of $24 each week.
Write an equation describing Sharon’s
weekly pay.
![Page 3: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/3.jpg)
Complete the table:
Hours Process Total Pay
0
1
2
3
x y
![Page 4: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/4.jpg)
Complete the table:
Hours Process Total Pay
0 8(0) + 24 24
1 8(1) + 24 32
2 8(2) + 24 40
3 8(3) + 24 48
x 8x + 24 y
![Page 5: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/5.jpg)
An equation to describe the total weekly earnings in terms of the number of
hours worked is…
y = 8x + 24
The amount Sharon needs to pay all of her bills must be less than
or equal to the amount she earns
![Page 6: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/6.jpg)
An inequality to describe the amount Sharon needs
to earn to pay her bills is …
8 24y x
Graph this Inequality
![Page 7: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/7.jpg)
Begin at the y-intercept
8 24y x
hours
Bills ($)
8
1 2 3 4 5
16243240
![Page 8: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/8.jpg)
Find a 2nd point with the slope
8 24y x
hours
Bills ($)
8
1 2 3 4 5
16243240
![Page 9: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/9.jpg)
Connect the points with a line
8 24y x
hours
Bills ($)
8
1 2 3 4 5
16243240
![Page 10: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/10.jpg)
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
![Page 11: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/11.jpg)
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
![Page 12: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/12.jpg)
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.
![Page 13: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/13.jpg)
The inequality shows the total miles,
y, is greater than 4x + 32
y > 4x + 32
Graph this inequality
![Page 14: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/14.jpg)
First Graph the y-intercept
4 32y x
days
Total Miles
4
1 2 3 4 5
812162432
3640
![Page 15: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/15.jpg)
Graph a second point
4 32y x
days
Total Miles
4
1 2 3 4 5
812162432
3640
![Page 16: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/16.jpg)
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
![Page 17: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/17.jpg)
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
![Page 18: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/18.jpg)
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
![Page 19: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/19.jpg)
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
![Page 20: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/20.jpg)
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
![Page 21: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/21.jpg)
To graph this inequality, we can use T and P
intercepts
6T + 2P < 120
T P0
0
![Page 22: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/22.jpg)
To graph this inequality, we can use T and P
intercepts
6T + 2P < 120
T P20 0
0 60
![Page 23: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/23.jpg)
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
![Page 24: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/24.jpg)
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
![Page 25: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/25.jpg)
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
![Page 26: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/26.jpg)
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?
![Page 27: In this lesson… We will write and graph linear inequalities](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d165503460f949eca4e/html5/thumbnails/27.jpg)
Complete Activity 6d
Write Linear Inequalities
Graph Linear Inequalities
Solve Problems using Linear Inequalities