Practice Dependent vs Independent Variables 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

The independent variable is chosen freely as input; the dependent variable's value is then determined by the function rule.

You choose the input (independent), and the function gives the output (dependent).

Showing a random 20 of 50 problems.

Example 1

hard
In y=12x, describe how the dependent variable responds as the independent variable triples.

Example 2

medium
Given y=3x−1, find the dependent value when the independent value is 4.

Example 3

medium
On a graph, which axis typically shows the independent variable?

Example 4

easy
In the equation d=60t (distance = speed × time), which is dependent?

Example 5

easy
In A=πr2, what is the independent variable?

Example 6

medium
In x=5−2y, if y is independent, express the dependent variable explicitly.

Example 7

easy
A water tank fills at a constant rate, V=5t (liters at time t minutes). Which is dependent?

Example 8

easy
In y=4x−7, name the dependent variable.

Example 9

medium
A taxi charges 3plus2 per mile: C=3+2m. Identify both variables and their roles.

Example 10

medium
In the data table input 1,2,3 → output 2,4,6, name the variables.

Example 11

challenge
A circle's area depends on radius. If the radius is the independent variable, find the rate-style ratio Ar2 and explain.

Example 12

challenge
Two quantities satisfy y=mx for unknown fixed m. Using the point (2,6), find m, then state which symbol is the parameter.

Example 13

medium
A scientist plots height versus age. Which axis holds age?

Example 14

challenge
In P=kV (fixed k), describe how the dependent variable responds as the independent one doubles.

Example 15

medium
If y depends on x via y=−2x+6, what happens to y when x increases by 1?

Example 16

challenge
A car's stopping distance is d=0.05v2 in meters. If a driver doubles their speed, by what factor does the dependent value d grow?

Example 17

medium
For a table with inputs 1,2,3,4 giving outputs 5,8,11,14, write the linear rule with x independent.

Example 18

medium
A coffee shop's daily revenue R depends on customers n: R=4.5n. Find n when R=270.

Example 19

medium
A phone plan costs C=30+0.10m dollars, where m is minutes used. Identify both variables and find C when m=200.

Example 20

easy
In h=2+3d where d is days, find the dependent value when d=4.
← Back to Dependent vs Independent Variables Worked Examples Formula Explained