Inverse proportion

When the relationship between $y$ and $x$ is of the form $y = \frac{m}{x}$ then $y$ and $x$ are inversely proportional to each other.

Inverse means reversed in behaviour. When two variables are inversely proportional doubling one leads to halving the other. In other words multiplying one by two would lead to dividing the other by two.

Let’s look at an example. $y = \frac{2}{x}$ . The values of $x$ and $y$ for $x = 1$ to $5$ are shown below.

If $x$ is doubled from $1$ to $2$ then $y$ is halved from $2$ to $1$ .

If $x$ is increased by a factor of $2.5$ from $2$ to $5$ then $y$ is reduced by a factor of $2.5$ from $1$ to $\frac{2}{5}$ .

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Equations and graphs

Inverse proportion