Transcript In this lesson…

In this lesson…
We will write and
graph linear
inequalities
Sharon earns $8 an hour
and a bonus of
$24 each week.
Write an equation
describing Sharon’s
weekly pay.
Complete the table:
Hours
0
1
2
3
x
Process
Total Pay
y
Complete the table:
Hours
0
Process
8(0) + 24
Total Pay
24
1
8(1) + 24
32
2
3
x
8(2) + 24
8(3) + 24
8x + 24
40
48
y
An equation to describe
the total weekly earnings
in terms of the number of
hours worked is…
y = 8x + 24
The amount Sharon needs to pay
all of her bills must be less than
or equal to the amount she earns
An inequality to
describe the amount
Sharon needs to earn
to pay her bills is …
y  8 x  24
Graph this Inequality
Begin at the y-intercept
y  8 x  24
Bills ($)
40
32
24
16
8
1
2
3
4
5
hours
Find a 2nd point with the slope
y  8 x  24
Bills ($)
40
32
24
16
8
1
2
3
4
5
hours
Connect the points with a line
y  8 x  24
Bills ($)
40
32
24
16
8
1
2
3
4
5
hours
Shade below the line
y  8 x  24
Bills ($)
40
32
24
16
8
1
2
3
4
5
The
shaded
region
represents
the the
amounts
Sharon
can afford
hours
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
y  4 x  32
Total Miles
40
36
32
24
16
12
8
4
1
2
3
4
5
days
Graph a second point
y  4 x  32
Total Miles
40
36
32
24
16
12
8
4
1
2
3
4
5
days
Connect with a dotted line
Total Miles
y  4 x  32
The points on
the line are not
included since
Paul must jog
MORE than
the amounts
on the line
40
36
32
24
16
12
8
4
1
2
3
4
5
days
Shade ABOVE the line
Total Miles
y  4 x  32
The shaded
region
represents
the miles
Paul must
run
40
36
32
24
16
12
8
4
1
2
3
4
5
days
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 Tshirts, 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
0
P
0
To graph this inequality,
we can use T and P
intercepts
6T + 2P < 120
T
20
P
0
0
60
Graph each ordered pair
6T + 2P < 120
Posters
60
50
40
30
20
T
20
P
0
0
60
10
5
10
15
20
25
T-Shirts
Connect with a dotted line
6T + 2P < 120
Posters
60
50
40
30
20
T
20
P
0
0
60
10
5
10
15
20
25
T-Shirts
Shade below the line
6T + 2P < 120
Posters
60
50
40
30
20
T
20
P
0
0
60
10
5
10
15
20
25
T-Shirts
The shaded region represents the
numbers of T-Shirts and Posters the
Student Council can afford
Posters
60
Can they
afford 15
T-Shirts
and 30
posters?
50
40
30
20
10
5
10
15
20
25
T-Shirts
Complete Activity 6d
Write Linear Inequalities
Graph Linear Inequalities
Solve Problems using
Linear Inequalities