Richard bought 50 tokens for the video arcade. Each game uses three tokens to play. Which linear function, if any, would represent the relationship between g, the number of games played and t, the number of tokens remaining?

A. t = 3g + 50
Incorrect. Since this relationship has a constant rate of change, it is a linear function. The number of games played, g, must be multiplied by 3 tokens per game. This value must be subtracted from 50 to get the number of tokens remaining, t.

B. t = 3g − 50
Incorrect. Since this relationship has a constant rate of change, it is a linear function. The number of games played, g, must be multiplied by 3 tokens per game. This value must be subtracted from 50 to get the number of tokens remaining, t.

C. t = 50 − 3g
Correct. Since this relationship has a constant rate of change, it is a linear function. The number of games played, g, must be multiplied by 3 tokens per game. This value must be subtracted from 50 to get the number of tokens remaining, t.

D. No linear function exists.
Incorrect. Since this relationship has a constant rate of change, it is a linear function. The number of games played, g, must be multiplied by 3 tokens per game. This value must be subtracted from 50 to get the number of tokens remaining, t.

Stephanie has $150 in her bank account. If she withdraws $5 a day without making additional deposits, which equation, if any, will shows the number of days, d, before Stephanie’s account has a balance of $25?

A. 25 = 150 − 5d
Correct! Since this relationship has a constant rate of change, it is a linear function. Five dollars a day must be multiplied by the number of days, d. This amount must be subtracted from the $150 in the bank account and equal to 25.

B. 25 = 150 + 5d
Incorrect. Since this relationship has a constant rate of change, it is a linear function. Five dollars a day must be multiplied by the number of days, d. This amount must be subtracted from the $150 in the bank account and equal to 25.

C. 25 = 150d + 5
Incorrect. Since this relationship has a constant rate of change, it is a linear function. Five dollars a day must be multiplied by the number of days, d. This amount must be subtracted from the $150 in the bank account and equal to 25.

D. No linear function exists.
Incorrect. Since this relationship has a constant rate of change, it is a linear function. Five dollars a day must be multiplied by the number of days, d. This amount must be subtracted from the $150 in the bank account and equal to 25.

The tables below show the cost of apples at local farmer’s markets. Which of the following tables best represents a linear relationship?

A.
Incorrect. This table is not a linear relationship. The number of apples changes by 10. The cost in dollars changes by 3, then by 5, then by 3, so this is not a linear relationship. The change in both sides of the table must be consistent.

B.
Correct! This table is a linear relationship because there is a constant rate of change. The number of apples changes by 10 and the cost changes by 5.50 in each row. Therefore the relationship is linear.

C.
Incorrect. This table is not a linear relationship. The number of apples changes by 10. The cost in dollars changes by 5, then by 6, then by 7, so this is not a linear relationship. The change in both sides of the table must be consistent.

D.
Incorrect. This table is not a linear relationship. The number of apples changes by 10. The cost in dollars changes by 5, then by 4, then by 3, so this is not a linear relationship. The change in both sides of the table must be consistent.

An arrow was shot into the air. The table below shows the height of the arrow at specific times after it was released.

Is the relationship between the time in the air and the height of the arrow a linear relationship?

A. Yes, because the relationship y = 2x + 5.
Incorrect. This function is true only when the arrow is released.

B. Yes, because the arrow will travel in a straight line.
Incorrect. Sketch a graph that represents the path of the arrow.

C. No, because there is not a constant rate of change.
Correct! During the first second the height increased by 15.1 meters but during the second second the height increased by only 5.3 meters.

D. No, because there is a constant rate of change.
Incorrect. There is not a constant rate of change, that makes the relationship nonlinear.