Constructing Linear Functions

Question 1

Richard and Gloria ran a 10-kilometer race. Gloria gave Richard a head start by letting him begin 2.2 kilometers in front of the start line. The distances of Richard and Gloria past the start line as the race progressed can be represented by linear functions and are shown in the table of values and graph below. Whose time was faster, and by how much?Richard’s Distance Past the Start LineTime (minutes)510152025Distance (kilometers)2.83.44.04.65.2

Revolt · Accepted Answer

Gloria’s time was 2.5 minutes faster.

Question 2

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?

Revolt · Accepted Answer

20 calories per minute

Question 3

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?

Revolt · Accepted Answer

$15 per hour

Question 4

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

Revolt · Accepted Answer

Mary is filling 36 cups per minute, which is faster than Jorge.

Question 5

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

Revolt · Accepted Answer

0.25 miles per minute

Question 6

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

Revolt · Accepted Answer

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.

Question 7

Eric received a gift card worth $25 as a birthday present. He is spending $2.50 per day using the gift card, as shown in the graph below. Which statement is true about the linear function that represents his gift card spending?

Revolt · Accepted Answer

The initial value is the amount on the gift card before Eric starts using it.

Question 8

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?

Revolt · Accepted Answer

$25

Question 9

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

Revolt · Accepted Answer

(18, 27), because the rate of change of the function is

Question 10

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?

Revolt · Accepted Answer

The initial values of the two functions are different, and the rates of change of the two functions are the same.

Constructing Linear Functions Answers

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