Direct & inverse proportion

Japanese school year: Junior high 1

What you learn

Learn direct proportion where the ratio between two quantities is constant, and inverse proportion where their product is constant, along with their graphs. These describe relationships like time and distance at constant speed, or rectangle dimensions with fixed area. Prior knowledge of coordinates and signed numbers helps your progress.

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Key points

This is the fundamental formula expressing that $y$ is directly proportional to $x$ . The constant $a$ is the constant of proportionality, and its graph is a line passing through the origin $(0, 0)$ .

y = ax

This formula shows that in direct proportion, the ratio of $y$ to $x$ is always the constant $a$ . It is used to find the constant of proportionality $a$ from a known pair of $x$ and $y$ .

\frac{y}{x} = a \quad (x \neq 0)

This formula represents the relationship where $y$ is inversely proportional to $x$ . The constant $a$ is the constant of proportionality, and the graph forms a hyperbola symmetric about the origin.

y = \frac{a}{x} \quad (x \neq 0)

This formula shows that in inverse proportion, the product of $x$ and $y$ always equals the constant $a$ . You can immediately find $a$ when one pair of $x$ and $y$ is known.

xy = a

Choose a set to practice.

Practice 1Coming soon