NAME _____________________________________________ DATE __________________ PERIOD _________
Lesson 6 Reteach
Construct Functions
The initial value of a function is the corresponding y-value when x equals 0. You can find the initial
value of a function from graphs, words, and tables.
Example 1
A football club is hiring a painter to paint a mural on the concession stand
wall. The painter charges an initial fee plus $25 an hour. After 12 hours of
work, the football club owed $350. Assume the relationship is linear. Find
and interpret the rate of change and initial value.
Since the painter charges $25 an hour, the rate of change is 25. To
find the initial value, use slope-intercept form to find the y-intercept.
y = mx + b
Slope-intercept form
y = 25x + b
Replace m with the rate of change, 25.
350 = 25(12) + b
50 = b
Replace y with 350 and x with 12.
Solve for b.
The y-intercept is 50. So, the initial fee is $50.
Copyright © The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.
Exercises
1. While hiking, Devon’s altitude rose 10 feet for every 5 minutes. After an hour of hiking,
his altitude was 295 feet. Assume the relationship is linear. Find and interpret the rate
of change and initial value.
2. A frozen dessert was placed in a freezer. Each hour, the temperature dropped 13 degrees.
Three hours later, the temperature was 32ºF. Assume the relationship is linear. Find
and interpret the rate of change and initial value.
3. Tyler charges his customers a weekly fee plus $5 every time he walks their dogs. One
week, he charged a customer $25 for walking their dog 3 times. Assume the relationship
is linear. Find and interpret the rate of change and initial value.
Course 3 • Chapter 4 Functions
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NAME _____________________________________________ DATE __________________ PERIOD _________
Lesson 6 Homework Practice
Construct Functions
Solve.
3. MOVIES Marcus is a member of a theater
club. He pays a monthly fee and his
movie tickets are then $5 for an
unlimited number of movies that month.
The graph shows the cost for each
month. Find the monthly fee.
Cost ($)
1. FUNDRAISING The Pep Club rented a
shaved ice machine to sell shaved ice as
a fundraiser. They paid an initial fee and
then an hourly charge. The table shows
the cost per hour. Find and interpret the
rate of change and initial value. Assume
the relationship between the two
quantities is linear.
Number of
Hours, x
2
3
4
5
Cost ($), y
30
35
40
45
30
27
24
21
18
15
12
9
6
3
0
(4, 27.50)
(3, 22.50)
(2, 17.50)
(1, 12.50)
1
2
3
4
5
Copyright © The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.
Number of Months
2. GARDENING Simone planted a tomato
plant and measured its height weekly.
The total height at 2, 3, 4, and 5 weeks
respectively were 13, 16, 19, and 22
inches tall. How tall was the tomato
plant when Simone planted it? Assume
the relationship is linear.
Course 3 • Chapter 4 Functions
4. PHOTOS The cost of having photos taken
includes a sitting fee and $12 for each
portrait. The cost of 3, 6, and 9 photos
respectively is $51, $87, and $123. What
is the sitting fee?
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