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OBJECTIVE
Students will understand how to
write and solve real world
application problems using
slope
Real World
Applications


Slope-Intercept Form
Standard Form
Slope-Intercept Form
Word problems with linear equations will be
in slope-intercept form if you are given the
following information:
•the slope (m) - the rate of change
•the y-intercept (b) - the starting (initial) value
Application
A closet organizer charges a $100 initial consultation fee
plus $30 per hour. The cost as a function of the number of
hours worked is graphed below.
a. Write an equation that
represents the cost as a
function of the number of
hours.
Cost
is
$30
y
=
30
for each
hour
An equation is y = 30x + 100.
•x
plus
$100
+
100
Continued
A closet organizer charges $100 initial consultation fee
plus $30 per hour. The cost as a function of the number of
hours worked is graphed below.
b. Identify the slope and y-intercept and
describe their meanings.
The y-intercept is 100. This is the cost for 0 hours, or the initial
fee of $100. The slope is 30. This is the rate of change of the
cost: $30 per hour.
c. Find the cost if the organizer works 12 hrs.
y = 30x + 100
= 30(12) + 100 = 460
Substitute 12 for x in the equation
The cost of the organizer for 12 hours is $460.
Try This!
A caterer charges a $200 fee plus $18 per person served. The
cost as a function of the number of guests is shown in the
graph.
a. Write an equation that represents
the cost as a function of the
number of guests.
Cost
is
$18
y
=
18
for each
meal
plus
$200
+
200
•x
An equation is y = 18x + 200.
Try This! Continued
A caterer charges a $200 fee plus $18 per person served. The
cost as a function of the number of guests is shown in the
graph.
b. Identify the slope and y-intercept and describe
their meanings.
The y-intercept is 200. This is the cost for 0 people, or the
initial fee of $200. The slope is 18. This is the rate of
change of the cost: $18 per person.
c. Find the cost of catering an event for 200 guests.
y = 18x + 200
= 18(200) + 200 = 3800
Substitute 200 for x in the equation
The cost of catering for 200 people is $3800.
More – finding slope with
formula
You will start your linear equation by finding
slope – how many points do you need to find
slope??? If you are given the following type of
information:
•A table of information
•Information that can be written as ordered pairs
Problem-Solving Application
The cost to stain a deck is a linear function of the
deck’s area. The cost to stain 100, 250, 400 square feet
are shown in the table. Write an equation in slopeintercept form that represents the function. Then find
the cost to stain a deck whose area is 75 square feet.
• The answer will have two parts—an equation in
slope-intercept form and the cost to stain an area
of 75 square feet.
• The ordered pairs given in the table—(100, 150),
(250, 337.50), (400, 525)—satisfy the equation.
Continued
You can use two of the ordered pairs to find the slope.
Then use point-slope form to write the equation. Finally,
write the equation in slope-intercept form.
Choose any two ordered pairs from the table
to find the slope.
Use (100, 150) and
(400, 525).
Substitute the slope and any ordered pair from
the table into y = mx + b
Continued
Write the equation in slope-intercept form.
Find the cost to stain an area of 75 sq. ft.
y = 1.25x + 25
y = 1.25(75) + 25 = 118.75
The cost of staining 75 sq. ft. is $118.75.
Continued
If the equation is correct, the ordered pairs that you
did not use in Step 2 will be solutions. Substitute (400,
525) and (250, 337.50) into the equation.
y = 1.25x + 25
525 1.25(400) + 25
525 500 + 25
525
525

y = 1.25x + 25
337.50
1.25(250) + 25
337.50
337.50
312.50 + 25
337.50 
Try This!
What if…? At a newspaper the costs
to place an ad for one week are
shown. Write an equation in slopeintercept form that represents this
linear function. Then find the cost of
an ad that is 21 lines long.
• The answer will have two parts—an equation in
slope-intercept form and the cost to run an ad
that is 21 lines long.
• The ordered pairs given in the table—(3, 12.75),
(5, 17.25),(10, 28.50)—satisfy the equation.
Try This! Continued
You can use two of the ordered pairs to find the slope.
Then use y = mx + b to find b
Step 1 Choose any two ordered pairs from the table to find
the slope.
Use (3, 12.75)
and (5, 17.25).
Step 2 Substitute the slope and any ordered pair from
the table
Try This! Continued
Write the equation in slope-intercept form by
solving for y.
Find the cost for an ad that is 21 lines long.
y = 2.25x + 6
y = 2.25(21) + 6 = 53.25
The cost of the ad 21 lines long is $53.25.
Try This! Continued
4
Look Back
If the equation is correct, the ordered pairs that
you did not use in Step 2 will be solutions.
Substitute (3, 12.75) and (10, 28.50) into the
equation.
y = 2.25x + 6
12.75 2.25(3) + 6
12.75 6.75 + 6
12.75 12.75 
y = 2.25x + 6
28.50
28.50
28.50
2.25(10) + 6
22.50 + 6
28.50 
Standard Form
You will write an equation in standard form if
you are given the following type of
information:
•Values for two types of items
•The values are combined to equal one total.
Application
The school sells pens for $2.00 and notebooks for $3.00.
The equation 2x + 3y = 60 describes the number of pens x
and notebooks y that you can buy for $60.
Graph the function and find its intercepts.
2x + 3y = 60
Find the intercepts.
x-intercept:
y-intercept:
2x + 3y = 60
2x + 3y = 60
2x + 0 = 60
2x = 60
x = 30
0 + 3y = 60
3y = 60
y = 20
x-intercept: 30; y-intercept: 20
Application
The school sells pens for $2.00 and notebooks for
$3.00. The equation 2x + 3y = 60 describes the number
of pens x and notebooks y that you can buy for $60.
What does each intercept represent?
x-intercept: 30. This is the
number of pens that can be
purchased if no notebooks are
purchased.
y-intercept: 20. This is the
number of notebooks that can
be purchased if no pens are
purchased.
Try This!
You are buying $20 worth of bird seed that consists of two
types of seed. Thistle seed costs $2 per pound and Dark Oil
Sunflower Seed costs $5 per pound. Write an equation that
represents the different amounts of each type of seed you
can buy. Graph this function by finding the intercepts. What
does each intercept represent?
The equation of the line will be:
2x + 5y = 20
x-intercept:
2x = 20
x = 10
y-intercept:
5y = 20
y=4
x-intercept: 10. This is the amount of
Thistle Seed that can be purchased if
no Sunflower Seed is purchased.
y-intercept: 4. This is the amount of
Sunflower Seed that can be purchased
if no Thistle Seed is purchased.