Functions Worksheet - Big Ideas Math Prealgebra: A Florida Standards Curriculum Teaching Edition Page 22
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47Comparing Linear Functions
4 4
EXAMPLE
The earnings y (in dollars) of a nighttime employee working x hours
are represented by the linear function y = 7.5x + 30. The table shows
the earnings of a daytime employee.
+1
+1
+1
Time (hours), x
1
2
3
4
Earnings (dollars), y
12.50
25.00
37.50
50.00
+12.50 +12.50 +12.50
a. Which employee has a higher hourly wage?
Nighttime Employee
Daytime Employee
change in earnings
$12.50
y = 7.5x + 30
=
——
—
change in time
1 hour
The slope is 7.5.
The nighttime employee
The daytime employee
earns $7.50 per hour.
earns $12.50 per hour.
So, the daytime employee has a higher hourly wage.
b. Write a linear function that relates the daytime employee’s
earnings to the number of hours worked. In the same coordinate
plane, graph the linear functions that represent the earnings of the
two employees. Interpret the graphs.
Employee Earnings
Use a verbal model to write a linear function that represents the
earnings of the daytime employee.
y
90
nighttime
Hourly
⋅
Hours
75
Earnings =
60
wage
worked
45
y = 12.5x
30
daytime
15
The graph shows that the daytime employee has a higher hourly
0
0
1
2
3
4
5
6
7 8
x
wage but does not earn more money than the nighttime
Time (hours)
employee until each person has worked more than 6 hours.
4. Manager A earns $15 per hour
Earnings of Manager B
and receives a $50 bonus. The
Exercise 14
y
graph shows the earnings of
125
Manager B.
100
75
(3, 75)
a. Which manager has a higher
50
hourly wage?
25
0
b. After how many hours does
0
1
2
3
4
5
6
7
x
Manager B earn more money
Time (hours)
than Manager A?
260
260
Chapter 6
Chapter 6
Functions
Functions
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