Inverse Proportion (Inverse Variation) and Its Graph
Big Idea
Have you ever noticed that if more workers share a job, each person works fewer hours? Or if you drive faster, you reach your destination in less time? These are examples of inverse proportion — when one quantity increases, the other decreases in a specific mathematical way.
📐 Formal Definition
Two quantities $x$ and $y$ are said to be inversely proportional (or in inverse variation) if their product is always a constant.
$$ y = \frac{k}{x} \quad \text{or equivalently} \quad xy = k $$
where $k$ is a non-zero constant called the constant of proportionality (or constant of variation).
We write this relationship as: $$ y \propto \frac{1}{x} $$
This is read as "$y$ is inversely proportional to $x$" or "$y$ varies inversely as $x$."