Proportion involving a stated power

When a question states that \(y\) is proportional to \(x^2\), write \(y=kx^2\) and find \(k\) from a known pair. For inverse proportion to \(x^2\), write \(y=\dfrac{k}{x^2}\). The quantity being scaled is \(x^2\), not \(x\).

Example

If \(y\propto x^2\) and \(y=45\) when \(x=3\), then \(k=\dfrac{45}{9}=5\). When \(x=5\), \(y=5(25)=125\).

If a positive quantity follows \(y=\dfrac{80}{x^2}\), doubling \(x\) makes \(y\) one quarter as large. At \(x=2\), \(y=20\); at \(x=4\), \(y=5\).

Use the relationship given or justified by the context. Do not choose a power merely because one pair of values fits it.