Practice Dependent vs Independent Variables in Math

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

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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=12xy = \frac{12}{x}, describe how the dependent variable responds as the independent variable triples.

Example 2

medium
Given y=3xโˆ’1y=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=60td = 60t (distance = speed ร— time), which is dependent?

Example 5

easy
In A=ฯ€r2A = \pi r^2, what is the independent variable?

Example 6

medium
In x=5โˆ’2yx=5-2y, if yy is independent, express the dependent variable explicitly.

Example 7

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

Example 8

easy
In y=4xโˆ’7y = 4x - 7, name the dependent variable.

Example 9

medium
A taxi charges 3plus3 plus 2 per mile: C=3+2mC=3+2m. Identify both variables and their roles.

Example 10

medium
In the data table input 1,2,3 โ†’ 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\frac{A}{r^2} and explain.

Example 12

challenge
Two quantities satisfy y=mxy=mx for unknown fixed mm. Using the point (2,6)(2,6), find mm, 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=kVP=\frac{k}{V} (fixed kk), describe how the dependent variable responds as the independent one doubles.

Example 15

medium
If yy depends on xx via y=โˆ’2x+6y = -2x + 6, what happens to yy when xx increases by 11?

Example 16

challenge
A car's stopping distance is d=0.05v2d = 0.05 v^2 in meters. If a driver doubles their speed, by what factor does the dependent value dd grow?

Example 17

medium
For a table with inputs 1,2,3,41, 2, 3, 4 giving outputs 5,8,11,145, 8, 11, 14, write the linear rule with xx independent.

Example 18

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

Example 19

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

Example 20

easy
In h=2+3dh = 2 + 3d where dd is days, find the dependent value when d=4d = 4.
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