Dependent vs Independent Variables Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Dependent vs Independent Variables.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept 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).

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: The dependent variable's value is controlled by and depends on what the independent variable is set to.

Common stuck point: By convention, the independent variable goes on the x-axis and the dependent on the y-axis — not the other way.

Sense of Study hint: Ask yourself: which quantity do I choose freely, and which is calculated from my choice?

Worked Examples

Example 1

easy
In y = 3x + 2, which variable is independent and which is dependent?

Solution

  1. 1
    The value of x is chosen freely—it is the independent variable.
  2. 2
    The value of y is determined by x—it is the dependent variable.
  3. 3
    We say 'y depends on x'.

Answer

x is independent; y is dependent.
The independent variable is the input (you choose it), and the dependent variable is the output (it is calculated from the input). In y = f(x), x is always independent.

Example 2

medium
A factory's cost is C = 500 + 8n where n is the number of units produced. Identify the variables.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

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

Example 2

medium
On a graph, which axis typically shows the independent variable?
← Back to Dependent vs Independent Variables Formula Explained Practice Mode

Background Knowledge

These ideas may be useful before you work through the harder examples.

function definitionvariables