Inverse proportion and a fixed product

\(y\) is inversely proportional to \(x\) when \(y=\dfrac kx\), with \(x\ne0\), so \(xy=k\) is constant. Multiplying \(x\) by a positive factor divides \(y\) by that factor. For positive quantities, the graph decreases and does not touch either axis.

Example

A fixed journey takes \(3\) hours at \(60\text{ km/h}\). Its distance is \(180\text{ km}\), so travelling time \(t=\dfrac{180}{v}\). At \(75\text{ km/h}\), \(t=2.4\text{ h}=2\text{ h}\hspace{0.5em}24\text{ min}\).

A decreasing relationship is not automatically inverse proportion; check that the product, rather than the sum, stays fixed.