Practice Linear Relationship in Math

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

Worksheet PDF Free Answer-key PDF Family

Quick Recap

A relationship between two variables where the rate of change is constant, producing a straight line when graphed. Expressed as y=mx+by = mx + b where mm 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−1y = 4x - 1, what is the slope?

Example 2

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

Example 3

medium
For the equation 2x+3y=122x + 3y = 12, find the slope and yy-intercept.

Example 4

medium
A taxi charges $3 base plus $2 per mile. Write the linear equation and find the cost for 55 miles.

Example 5

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

Example 6

hard
A line has slope 23\tfrac{2}{3} and passes through (−3,−1)(-3, -1). Find the equation and the xx-intercept.

Example 7

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

Example 8

hard
A line passes through (−2,5)(-2, 5) and (4,−7)(4, -7). Find the value of yy when x=0x = 0 (the yy-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)(1, 5) and (3,11)(3, 11). Find the equation of the line in y=mx+by = mx + b form.

Example 11

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

Example 12

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

Example 13

medium
A candle burns down linearly: 2020 cm tall at 00 hours, 1414 cm at 33 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)(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 22 hours it has 4040 gallons; after 55 hours it has 100100 gallons. What is the rate (gallons per hour)?

Example 16

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

Example 17

medium
A line has xx-intercept 44 and yy-intercept −6-6. Find the equation in y=mx+by = mx + b form.

Example 18

easy
A table adds 55 to yy each time xx rises by 11. Is it linear?

Example 19

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

Example 20

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