Practice Constant Rate 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 constant rate of change means the output increases (or decreases) by the same fixed amount for every unit increase in the input — the hallmark of a linear function.

Constant rate means steady, uniform progress — like a car traveling at a fixed speed: every hour, the same number of miles is added to the total.

Showing a random 20 of 50 problems.

Example 1

medium
A line passes through (−2,5) and (4,−7). Find the constant rate of change.

Example 2

challenge
A line has constant rate m, passes through (1,7), and f(4)=19. Find m and f(0).

Example 3

medium
A line drops from (0,20) to (4,8). Find its constant rate.

Example 4

medium
A table shows (0,4),(2,10),(4,16). Find the constant rate per unit input.

Example 5

easy
A vertical line has what kind of rate of change?

Example 6

medium
Verify whether (1,3),(2,5),(3,8) has a constant rate.

Example 7

hard
A printer prints at 20 pages/min. After how many minutes will it have printed 130 pages, given 10 are already in the tray at start?

Example 8

medium
If a function's average rate of change between any two points is always the same value m, what type of function is it?

Example 9

hard
A car decelerates at a constant rate, slowing from 30 m/s to 0 m/s in 6 s. Find the rate of change of velocity.

Example 10

medium
A 12-cup coffee maker brews at a constant rate, finishing in 6 minutes. Find the rate in cups/min.

Example 11

easy
For y=−3x+7, what is the rate of change?

Example 12

challenge
A cyclist rides at constant 12 mph. A runner 5 miles ahead moves the same direction at constant 4 mph. When does the cyclist catch the runner?

Example 13

challenge
Two runners start together. A runs at constant 6 mph, B at constant 8 mph. After how long is B exactly 1 mile ahead?

Example 14

hard
A car travels at 40 mi/h for 2 hours and then at 60 mi/h for 3 hours. Is the trip a constant-rate motion? What is the average rate?

Example 15

easy
If the rate is −2 per unit, is the output increasing or decreasing?

Example 16

medium
A tank drains at a constant rate, going from 100 L to 40 L in 3 minutes. Find the rate.

Example 17

medium
A line has constant rate −12 and passes through (0,6). Find f(10).

Example 18

medium
Check whether y=x2 has a constant rate of change on [0,4].

Example 19

medium
If f has constant rate 4 and f(0)=2, find f(10).

Example 20

medium
Find the equation of the line passing through (2,5) and (6,13), interpret the slope, and write it in slope-intercept form y=mx+b.
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