AnswersNC-Foundations of Math 1 Fall 2nd 9 WeeksConstructing Linear Functions

Constructing Linear Functions Answers

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The table of values below represents a linear function and shows the number of miles on the odometer of Brian’s moped since he started riding it. What is Brian’s speed?Miles on the Odometer of Brian’s MopedNumber of Minutes Brian Has Been Riding Moped0481216Number of Miles Traveled3.254.255.256.257.25

A
0.25 miles per minute
B
1 mile per minute
C
3.25 miles per minute
D
4 miles per minute
2
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Jorge and Mary are both filling cups with fruit punch in preparation for a party. After 3 minutes, Jorge had 53 cups left to be filled, and after 5 minutes, he had 25 cups left to be filled. Mary’s progress is shown in the table of values below. Assuming that both Jorge and Mary are filling cups at a constant rate, which statement is correct?Mary’s Cup-Filling ProgressTime (minutes)0.511.522.5Cups Remaining9981634527

A
Jorge is filling 14 cups per minute, which is faster than Mary.
B
Jorge is filling 28 cups per minute, which is faster than Mary.
C
Mary is filling 18 cups per minute, which is faster than Jorge.
D
Mary is filling 36 cups per minute, which is faster than Jorge.
3

Linear function A and linear function B both have the same input values as shown below. Why will the output values for linear function A always be different than the corresponding output values for linear function B?

Question illustration
A
The initial values of the two functions are different, and the rates of change of the two functions are also different.
B
The initial values of the two functions are different, and the rates of change of the two functions are the same.
C
The initial values of the two functions are the same, and the rates of change of the two functions are different.
D
The initial values of the two functions are the same, and the rates of change of the two functions are also the same.
4

The linear function graphed below represents the value of a comic book since Lucy purchased it. What was the value of the comic book when Lucy bought it?

Question illustration
A
$10
B
$15
C
$25
D
$40
5

The table of values below represents a linear function and shows the amount of money in Juanita’s savings account since she began her part-time job. What is her monthly rate of savings?Amount in Juanita’s Savings AccountNumber of Months Working at Part-Time Job02468Amount in Savings Account (in dollars)$36$60$84$108$132

A
$12 per month
B
$18 per month
C
$24 per month
D
$36 per month
6

The linear function graphed below represents Tim’s age in the years since he was married. Which of these statements is correct?

Question illustration
A
The initial value is 22, and the rate of change is 1.
B
The initial value is 22, and the rate of change is 15.
C
The initial value is 32, and the rate of change is 1.
D
The initial value is 32, and the rate of change is 15.
7

The table of values below represents a linear function and shows the weight of a kitten as it has grown. What is the output for the initial value?Weight of a KittenKitten’s Age (weeks)246810Weight (pounds)0.81.42.02.63.2

A
0.2 pounds
B
0.3 pounds
C
0.6 pounds
D
0.8 pounds
8

The table of values shown below represents a linear function. Which of these points could also be an ordered pair in the table, and why?x036912y37111519

A
(18, 27), because the rate of change of the function is
Option A
B
(18, 27), because the rate of change of the function is
Option B
C
(27, 18), because the rate of change of the function is
Option C
D
(27, 18), because the rate of change of the function is
Option D
9

The table of values below represents a linear function and shows Marco’s progress as he is pumping gas into his car. What is the output for the initial value?Gas in Marco’s CarSeconds Spent Pumping Gas012243648Gallons of Gas in Car357911

A
0 gallons
B
2 gallons
C
3 gallons
D
6 gallons
10

Corinne and Aretha are having a 26-mile race. Corinne gave Aretha a head start by letting her begin 3.5 miles in front of the start line. Their distances past the start line as the race has progressed can be represented by linear functions and are shown in the table and graph below. How many minutes after the start of the race will Corinne catch Aretha?Corinne’s Distance Past the Start LineTime (minutes)1020304050Distance (miles)1.252.53.755.06.25

Question illustration
A
140 minutes
B
180 minutes
C
208 minutes
D
225 minutes
11

Royce is taking violin lessons. The instructor charges an initial fee and an hourly fee. The amount Royce pays based on the length of his lesson is shown in the graph below. What is the instructor’s hourly fee?

Question illustration
A
$15 per hour
B
$22 per hour
C
$26 per hour
D
$37 per hour
12

A computer had 2 gigabytes of data stored on it when Jackie bought it, and she is storing an additional 3.5 gigabytes per year, as shown in the table below. Which of these statements is correct about the linear function that represents this situation?Amount of Data Stored on Jackie’s ComputerTime (year)01234Gigabytes of Data22 + 3.5 = 5.55.5 + 3.5 = 99 + 3.5 = 12.512.5 + 3.5 = 16

A
The initial value represents the 2 gigabytes of data stored on the computer when Jackie bought it, and the rate of change represents the 3.5 gigabytes per year that Jackie is storing.
B
The initial value represents the 2 gigabytes per year that Jackie is storing, and the rate of change represents the 3.5 gigabytes of data stored on the computer when Jackie bought it.
C
The initial value represents the 3.5 gigabytes of data stored on the computer when Jackie bought it, and the rate of change represents the 2 gigabytes per year that Jackie is storing.
D
The initial value represents the 3.5 gigabytes per year that Jackie is storing, and the rate of change represents the 2 gigabytes of data stored on the computer when Jackie bought it.
13

The linear function graphed below represents Brenda’s monthly cell phone bill based on the number of hours she uses. What is her hourly rate?

Question illustration
A
$12 per hour
B
$15 per hour
C
$27 per hour
D
$39 per hour
14

During 30 minutes on the treadmill, LaToya burned 20 calories per minute. What is the rate of change of the function that represents this situation?

A
10 calories per minute
B
20 calories per minute
C
30 calories per minute
D
50 calories per minute
15

The linear function graphed below represents the height of a stalk of corn since a farmer began using a new fertilizer. What is the initial value?

Question illustration
A
0 feet
B
1 foot
C
4 feet
D
6 feet

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