Practice Proportional Function in Math

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

Quick Recap

A proportional function has the form f(x) = kx for a constant k \neq 0 — it passes through the origin and the ratio f(x)/x = k is constant.

Double the input, double the output. No offset—starts at zero.

Example 1

easy
The weight of water is proportional to its volume. 5 liters weighs 5 kg. Write the function, find the constant of proportionality k, and compute the weight of 8.5 liters.

Example 2

medium
Determine whether y is proportional to x given the table: x: 2, 4, 6 and y: 7, 14, 21. If yes, find k and the equation.

Example 3

easy
Hooke's Law states spring force is proportional to stretch: F = kx. If F = 30 N when x = 6 cm, find k and the force when x = 10 cm.

Example 4

medium
Explain why f(x) = 3x + 2 is NOT a proportional function, and find the value of b that would make g(x) = 3x + b proportional.
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