October 2026 - Dependent & Independent Variables Study Guide

Which is which

Three ways to identify them

Any of these will settle it, and they agree.

• The sentence test — "X depends on Y" makes X dependent and Y independent.
• The control test — the variable you could set in advance is independent. Time is almost always independent, because you cannot make it respond to anything.
• The function test — in y = 4x + 10, whatever you substitute for is independent. You choose x; y comes out.

Naming variables in a word problem

Reading a function as a rule

In y = 4x + 10, the 4 is the rate — how much y changes for each unit of x — and the 10 is where y starts when x is zero. Given a word problem, the fixed amount is the constant and the per-unit amount is the coefficient.

A call-out charge of £10 plus £4 for every mile is exactly this function. The number of miles is independent, the total cost is dependent, and the question of what happens at zero miles is answered by the constant.

Terms to know

Independent variable

The variable that is changed or controlled — the input.

Dependent variable

The variable measured in response — the output.

Controlled variable

A factor deliberately held constant so it cannot affect the result.

Function

A rule assigning exactly one output to each input.

Input

A value substituted for the independent variable.

Output

The value the function returns.

What the TEAS asks most

The same core ideas appear in different wording. If you can answer these without stopping to think, you have what this section requires.

Key points

• The dependent variable depends on the independent one.
• Independent goes on the x-axis, dependent on the y-axis.
• The variable you can set in advance is independent; time nearly always is.
• In y = mx + c, x is independent, y is dependent, m is the rate and c is the starting value.
• Which variable sits on which axis reflects the study design, not proof of cause.