WorksheetsProportional and Linear Relationships
Total questions: 60
Worksheet time: 2hrs 40mins
The change in rise over run on a graph is called the...
slant
slope
y-intercept
x-intercept
The location where the line crosses the y-axis is called the...
slant
slope
y-intercept
x-intercept
Which variable in the equation y = mx + b represents the slope?
y
m
x
b
Which variable in the equation y = mx + b represents the y-intercept?
y
m
x
b
Does this graph represent a positive or negative slope?
Positive
Negative
Does this graph represent a positive or negative slope?
Positive
Negative
Is this graph linear?
Linear
Nonlinear
Is this graph linear or nonlinear?
Linear
Nonlinear
Is this table linear or not linear?
Not Linear
Linear
Proportional
Non-proportional
The equation for a linear relationship is y = mx + b.
True
False
Olivia and Sophia are on a treasure hunt! They need to find the slope of the mysterious line shown in the graph to unlock the next clue. Can you help them by finding the slope?
-5/4
5/4
-4/5
4/5
Give the equation for the graph.
y = 5x - 3
y = 4x + 2
y = -2x + 5
y = -2x + 4
What is the y-intercept in the equation y = -2x + 5?
-2
3
5
Cannot be determined
Olivia and Ethan are playing a game with numbers! They have a table of values, and they need to find out which magical equation matches it. Can you help them solve the mystery?
Which equation matches the table?
y = x + 5
y = 5x
y = x - 5
x = y - 5
Is this table proportional or non-proportional?
non-proportional
proportional
Benjamin and Aria are on a treasure hunt! They found a mysterious map with a red line drawn on a grid. Can you help them by writing the equation of the line?
y = -1x + 3
y = 4x + 3
y = \(\frac{1}{4}x + 3\)
y = -4x + 3
Determine the equation for the linear relationship.
HINT: Find the slope (m) and the y-intercept (b). Then build the equation in slope-intercept form ( y=mx+b ).
y=4x+4
y=−2x−5
y=23x−2
y=−2x+23
Abigail and Isla are organizing a bake sale to raise funds for their school trip. They spent $30 on supplies and decided to sell each cookie for $2.
Can you help them figure out the slope of this linear relationship?
30
-30
2
-2
Grace and Mason are organizing a bake sale to raise funds for their school trip. They spent $30 on supplies and decided to sell each cookie for $2.
Can you help them figure out the y-intercept for this linear relationship?
30
-30
2
-2
Olivia and Charlotte are planning a road trip and they want to calculate the slope of the hill they will be driving up. If they know two points on the hill, how can they find the slope?
m=y−yx−x
y=mx+b
a2+b2=c2
m=x−xy−y
Mary walked at a steady pace toward the car.
Rohan and Anika are racing toy cars on a track that looks like a line on a graph! Can you help them find the slope of the track in simplest form?
1/4
4
-1/4
-4
Michael and Mia are tracking the water level in their backyard pond. They recorded the water loss over several weeks in the table below. Can you help them find the rate of change?
-1.5 cm/week
1.5 cm/week
-1/5 cm/week
1/5 cm/week
Find the slope given the two points (-4, 10) and (-6, 8).
-2
2
-1
1
What is the slope formula?
Write the equation that represents this word problem:
Marsha gets a job that pays $15 per hour, and she started the week with $20.
y = 15x + 20
y = 20x + 15
y = 15 + 20
y = 20 + 15
Answer Not Here
Elijah is a taco-making superstar at his local restaurant. He's already crafted 8 delicious tacos and can whip up 3 more tacos every minute. Can you help Elijah by writing the equation that represents his taco-making skills?
y = 8x + 3x
y = 3x + 8
y = 8x + 3
y = 3 + 8
Answer Not Here
What is the rate of change (unit rate) for the following graph?
80
20
40
160
Find the equation of the line in slope-intercept form.
y = 1/2x + 4
y = -2x - 4
y = -4x - 2
y = -1/2x - 4
Is the function represented by the graph linear or nonlinear?
linear
nonlinear
Becky's Shower
Rachel's Shower
They use the same amount of water
Abigail loves babysitting and earns $8.25 for every hour she spends with the kids. Which of the following equations can be used to represent this fun-filled job if h represents the hours she babysits, and t represents the total amount she earns?
t = 8.2h
t = 8.25h
h = 8.2t
h = 8.25t
Avery and Benjamin are watching a sloth race! The graph shows the speed of Sally the sloth. Meanwhile, Jordan, another sloth, is cruising at 3 ft per minute. Which sloth is winning the race?
Sally
Jordan
Impossible to tell
In a thrilling race around the gym, Jack and Harper were running laps. Who was the speedster, and by how many laps did they outpace the other after 6 minutes?
Jack is the speedster, and after 6 minutes he will have run 8 more laps.
Harper is the speedster, and after 6 minutes he will have run 8 more laps.
Impossible to tell.
Determine the constant of proportionality (slope) for the table. Express your answer as y = kx.
y = 1/2x
x = 1/2y
y = 2x
k = x
Is the graph proportional or non-proportional?
proportional
non-proportional
Proportional
Non-proportional
Clare owns a mobile pet grooming company. She charges $20 to come to your home plus $30 per hour to groom your pet. Which table models the amount she charges over time?
What is the function that represents the data in this table?
y=3x−1
y=−9x−1
y=31x+2
y=−31x−9
Abigail is organizing a fun baseball event and wants to surprise her team with custom shirts. She'll pay $9.50 for each shirt, plus a one-time fee of $22.50 for the awesome design.
What equation can be used to find y, the total cost to buy x shirts?
y=9.5x+22.5
y=22.5x+9.5
y=9.5x−22.5
y=22.5x−9.5
A bottle contains 30 fluid ounces of orange juice and 18 fluid ounces of pineapple juice. Which graph best represents the ratio of orange juice to pineapple juice in this bottle?
Which of the graphs shown match the table?
Which of these graphs correctly represents the equation y=2x
Tom, Liam, and Elijah are on a mission to save money for a fun adventure! The following table shows Tom's savings account. Can you figure out how much money Tom deposited when he opened the savings account?
$0
$5
$10
$15
Select the INCORRECT statement about this scenario given the graph.
The starting height of the banana tree is 8 inches.
The tree is growing consistently each day.
This is an example of a proportional relationship.
The tree grows 4 inches each day.
At day 3, the banana tree was 20 inches in height.
Which equation matches this situation:
Cameron's lunch account started at $50. He withdrew $3 a day for lunch.
A = account balance
d = day
d = $3A - 50
A = 53d
A = 50 - 3d
A = 3d + 50
What is the rate of change in the table?
1
7
-7
0
What is the rate of change (slope) of the following graph?
80
20
40
160
James and Arjun were watching the rain from their window. They decided to measure how fast it was falling. Can you help them figure out the rate of rainfall?
2 cm per hour
1/4 cm per hour
1/2 cm per hour
4 cm per hour
During a fun bus ride, Samuel and Abigail were counting students. What does the y-intercept represent in this graph?
Every minute, 60 students got off the bus.
There were 60 students to start with on the bus ride.
Each minute, 10 students got off the bus.
60 students rode the bus every minute.
What is the equation for the table?
y = \frac{1}{4}x - 3
y = 4x - 3
y = -3x - 3
y = -2x - 3
Which equation matches the table below?
y = x + 5
y = 5x
y = x - 5
x = y - 5
Write the equation of the line.
y = -1x + 3
y = 4x + 3
y = \frac{1}{4}x + 3
y = -4x + 3
What is the equation of this line?
y = x - 2
y = x + 2
y = 2x
y = -x + 2
What is the slope of the line represented by the equation y = 3x - 7?
3
7
-3
-7
Maya is drawing lines on a graph. She wants to draw a line that crosses the y-axis at 4. Which of the following equations should she use?
y = x - 4
y = 4x + 2
y = 2x + 4
y = -3x - 4
Given the points (2, 5) and (4, 9), what is the slope of the line that passes through them?
3
4
1
2
