Math Proportional & Nonproportional

Ethan is saving money to buy a new bicycle. He already has $40 saved. Each week, he earns $8 for mowing his neighbor’s lawn. Which equation can be used to find y, the total amount of money Ethan will have saved after mowing the lawn x times?

• y = 40 + 8x

• y = 40x + 8

• y = 8x − 40

• y = 40x

A water tank is being filled at a constant rate, as shown in the table below. What is the rate of change in liters per minute?

The table below shows a linear relationship between x and y. Create an equation that describes the relationship shown in the table.

A student in a foreign language program learns 15 new words each week. Which graph best represents the relationship between x, the number of weeks the student has been in the program and y, the total number of new words the student has learned?

• F

• G

• H

• J

Silas wrote an equation to model the total cost of his taxi ride.

- The base fare for the taxi ride is $2.55. - The taxi service charges $1.75 per mile. Which equation models Silas’s total cost in dollars, y, for a taxi ride that is x miles long?

• y = 2.55x – 1.75

• y = 2.55x + 1.75

• y = 1.75x – 2.55

• y = 1.75x + 2.55

The table below shows the cost of a gym membership based on the number of months enrolled. What is the constant of proportionality that relates the total cost, y, to the number of months, x?

• 150

• -50

• 50

• 25

Nicole had a collection of 60 stuffed animals. She gave away 5 stuffed animals per month until all her stuffed animals were gone. Which graph best represents this situation?

• A

• B

• C

• D

Which of the following graphs shows a line where each value of y is three more than half of x?

• Top Left

• Top Right

• Bottom Left

• Bottom Right

A runner maintains a constant speed of 50 miles per hour. Which of the following does not represent the distance the runner can run at this rate?

• y = 50x, where x represents the time in hours and y represents the distance in miles.

• Graph showing distance over time.

• Table showing distance run by runner.

• In 6 hours, a runner can run a distance of 225

Jeremiah is ordering custom water bottles for his basketball team. Each water bottle costs $12.75. The total cost of the order, y, is based on the number of bottles purchased, x, plus a one-time setup fee of $35 for customization. Which THREE statements are true about the relationship between x and y?

• The relationship between x and y is linear.

• The total cost can be represented by the equation y = 12.75x + 35.

• The constant rate of change in the cost per bottle is $12.75.

• The total cost decreases as more bottles are purchased.

• The total cost can be represented by the equation y = 12.75 + 35x