Free Printable Linear Relationships

Worksheets

Linear Relationships - Tables & Graphs

Total questions: 25

Worksheet time: 2hrs 5mins

Name

Class

Date

Does this graph show a proportional relationship?

Yes, because it is linear

Yes, because it is linear and goes through the origin.

No, because it is not linear

No, because it does not go through the origin.

Proportional relationships must go through the origin. (0,0)

True

False

Which of these terms is NOT used to describe the "m" in the equation y=mx+b.

Constant rate of change

starting point

unit rate

Constant of proportionality

Find the constant rate of change.

1/2

-1/2

-2

Johnny went to the carnival. It cost $7 to get in and $2 for every ticket.

Which equation would match this verbal description?

y = 2x

y = 7x + 2

y = 7x

y = 2x + 7

Billy opened a bank account with $200, and every week he spends $15.

Which equation best represents this situation?

y = -15x + 200

y = 15x - 200

y = 200x + 15

y = 15x + 200

What is the equation for the graph?

y=-3x

y=-3x-3

y=-3x+3

What is the equation for the graph?

$y=\frac{1}{3}x+3$

$y=\frac{1}{3}x-3$

$y=-\frac{1}{3}x-3$

$y=-\frac{1}{3}x+3$

What is the equation for the graph?

$y=\frac{1}{3}x+1$

$y=-\frac{1}{3}x-1$

$y=-\frac{1}{3}x+3$

$y=\frac{1}{3}x+3$

10.

Caden has 1 pen for every 3 pencils. He graphs this relationship with x representing the number of pens and y representing the number of pencils. Which statement is true about the graph? Select two answers.

The slope of the graph is $\frac{1}{3}.$

The slope of the graph is 3.

11.

Connor has 1 chocolate candy for every 2 strawberry waffles. He graphs this situation with x representing the number of chocolate candies and y representing the number of strawberry waffles. Which graph represents this statement and which statement is true? Select two answers.

The slope of the graph representing this situation is $\frac{1}{2}.$

The slope of the graph representing this situation is 2.

12.

Gracie has 1 bag of Hot Fries for every 4 bags of Skittles. She graphs this situation with x representing bags of Hot Fries and y representing bags of Skittles. Which graph correctly represents this situation and which statement is true? Select two answers.

The slope of the graph representing this situation is 4.

The slope of the graph representing this situation is $\frac{1}{4}.$

13.

Tyler and Landon each rent a canoe. The cost of Tyler's rental can be represented by the equation y=10x. Landon's rental is shown in the graph. Determine who pays more per hour for the canoe rental AND how much each person pays per hour. Select two answers.

Tyler pays more per hour.

Landon pays more per hour.

Tyler pays $10 per hour.

Landon pays $12 per hour.

Tyler pays $12 per hour.

14.

Alison and Lauren are both driving for a vacation. Alison's distance per hour is represented by the equation y=45x where x is the number of hours and y is the total distance. Lauren's driving is represented in the graph. Who drives at a greater speed per hour AND by how much? Select two answers.

Alison drives a greater distance per hour.

Lauren drives 92 miles per hour.

Lauren drives a greater distance per hour.

Alison drives 5 miles per hour faster than Lauren.

Lauren drives 1 mile per hour faster than Alison.

15.

Matthew and Layne both download music. Matthew's downloads are represented by the equation y=4x where x represents the number of minutes and y represents the total number of songs downloaded. Layne's downloads are represented in the graph. Select ALL true statements.

Layne downloads more songs per minute than Matthew.

Matthew downloads more songs per minute than Layne.

Layne downloads 4 songs per minute.

Mathew downloads 4 songs per minute.

Layne downloads 2 songs per minute.

16.

A kayak rental service charges $5 for a life jacket and $7.50 per hour to rent a kayak. What is the correct equation that represents this situation?

y = 5x + 7.50

y = - 7.50x - 5

y = 7.50x + 5

x = 7.50y + 5

17.

The graph shows the value of a machine over a 10-year period. Which equation best represents the relationship between x, the age of the machine in years, and y, the value of the machine in dollars, over this 10-year period?

y = - 0.002x + 2,500

y = - 500x + 8,000

y = 500x + 8,000

y = 0.002x + 2,500

18.

The graph shows the relationship between the number of hours a paddleboat is rented and the total cost of the rental. Write and equation for the relationship, then use the equation to predict how much it would cost to rent a paddleboat for 5.5 hours.

x = 20y + 30; $140

y = 30x + 20; $185

y = 20x -30; $80

y = 20x + 30; $140

19.

How is the constant of proportionality calculated?

Divide x by y.

Divide y by x.

Find the difference in the y-values and divide it by the difference in the x-values.

Find the difference in the x-values and divide it by the difference in the y-values.

20.

How is the slope calculated?

Divide x by y.

Divide y by x.

Find the difference in the y-values and divide it by the difference in the x-values.

Find the difference in the x-values and divide it by the difference in the y-values.

21.

Which equation best represents the relationship between the x values and the y values in the table?

y = 2x +12

y = 4x + 6

y = 2x + 4

y = 6x + 4

22.

John is having a new deck built. He paid $485 for the required materials, and he will pay his brother $25 an hour to build the deck. Which table shows the relationship between h, the number of hours John's brother works, and c, the total cost of the project.