The idea

Proportion with squares, cubes and roots

Why y ∝ x², y ∝ √x and y ∝ 1/x² all follow the same three-step method — write the equation, find k, use it — and how the power changes the scaling.

A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.

In this lesson — start anywhere

Ratio, proportion & rates of change · Direct & inverse proportion

Why y ∝ x², y ∝ √x and y ∝ 1/x² all follow the same three-step method — write the equation, find k, use it — and how the power changes the scaling.

Proportion doesn't have to be to

x

itself —

y

can be proportional to

x^2

, to

x^3

, to

\sqrt{x}

, or inversely to any of them. The wording maps directly to an equation:

words	equation
$y$ is proportional to the square of $x$	$y = kx^2$
$y$ is proportional to the square root of $x$	$y = k\sqrt{x}$
$y$ is inversely proportional to the square of $x$	$y = \dfrac{k}{x^2}$

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The rest of the explanation, plus 2 worked examples you step through move by move.

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