MathematicsFreePrintable

Linear Relationships Exploration

A free mathematics worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.

Download now

Name:Date:

Linear Relationships Exploration

Use y = mx + b to identify the rate of change and starting value. Show your work where asked.

Reading Linear Equations

1.In the equation y = 5x − 3, what are the slope and y-intercept?

Slope −3; y-intercept 5
Slope 5; y-intercept −3
Slope 2; y-intercept 0
Slope 5; y-intercept 3

2.A bike rental costs $8 to start, then $4 for each hour. Let x be the number of hours and y the total cost in dollars. Which equation models the cost?

y = 8x + 4
y = 4x + 8
y = 12x
y = 4x − 8

3.A line is described by y = −2x + 6. As x increases, which way does the line move from left to right?

Upward
Downward
It stays horizontal
It is vertical

4.Use y = −3x + 7 to complete the table. Give the y-value for each listed x-value.

x: 0 | 1 | 2 | 3

y: ___ | ___ | ___ | ___

Describing and Comparing Relationships

5.Describe a real-world meaning for y = 3x + 5. Explain what the 3 and the 5 could represent.

6.A storage locker costs $18 per week, plus a one-time setup charge of $12. Write an equation for the total cost y after x weeks.

7.Compare y = 4x + 2 and y = 4x + 7. How are their slopes related, and how will their graphs be positioned relative to each other?

8.Two lines have the same y-intercept. One has slope 1 and the other slope 3. Which line rises more steeply as x increases? Explain.

Apply and Create

9.A music service charges $24 per month and an extra $0.08 for each song download. In one month, Brianna downloads 150 songs. What is the total charge? Show your calculation.

10.Create a real-world situation that can be modeled by y = mx + b. State what x and y represent, identify the rate m and starting value b, and write a matching equation.