Practice Linear Relationship in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A relationship between two variables where the rate of change is constant, producing a straight line when graphed. Expressed as y=mx+b where m is the slope.

Add the same amount each step. Like paying $10/month—increase is constant.

Showing a random 20 of 50 problems.

Example 1

easy
In y=4x−1, what is the slope?

Example 2

challenge
A line and a proportional relation both pass through (4,12). The line also passes through (0,4). Find both equations.

Example 3

medium
For the equation 2x+3y=12, find the slope and y-intercept.

Example 4

medium
A taxi charges $3 base plus $2 per mile. Write the linear equation and find the cost for 5 miles.

Example 5

easy
Is y=7 (a horizontal line) linear?

Example 6

hard
A line has slope 23 and passes through (−3,−1). Find the equation and the x-intercept.

Example 7

challenge
A linear function f satisfies f(3)=11 and f(7)=23. Find f(100).

Example 8

hard
A line passes through (−2,5) and (4,−7). Find the value of y when x=0 (the y-intercept).

Example 9

medium
A gym charges a $50 sign-up fee plus $30 per month. After how many months will the total cost be $260?

Example 10

medium
Two points on a line are (1,5) and (3,11). Find the equation of the line in y=mx+b form.

Example 11

easy
A taxi charges a $3 base fee plus $2 per mile. Write the equation for total cost C in terms of miles m. Identify slope and y-intercept.

Example 12

easy
Does the line y=2x+3 pass through the origin?

Example 13

medium
A candle burns down linearly: 20 cm tall at 0 hours, 14 cm at 3 hours. Find the burn rate and the equation.

Example 14

medium
A linear table has (x,y)=(0,7),(1,4),(2,1),(3,−2). Write the equation.

Example 15

easy
A pool is filled at a constant rate. After 2 hours it has 40 gallons; after 5 hours it has 100 gallons. What is the rate (gallons per hour)?

Example 16

hard
Lines A and B both pass through (4,10). Line A also passes through (0,2) and is linear but not proportional. Line B is proportional. Find both equations.

Example 17

medium
A line has x-intercept 4 and y-intercept −6. Find the equation in y=mx+b form.

Example 18

easy
A table adds 5 to y each time x rises by 1. Is it linear?

Example 19

hard
A line passes through (1,4) and is parallel to y=−3x+7. Find its equation.

Example 20

medium
A table: (x,y)=(0,1),(1,4),(2,7),(3,10). Is it linear? Give the equation.
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