Inversely proportional

Definition

Two quantities are inversely proportional if their product is constant. When one quantity increases, the other decreases in such a way that their product remains unchanged.

5 Must Know Facts For Your Next Test

1. In an inversely proportional relationship, if one variable doubles, the other variable is halved.
2. The formula for two variables that are inversely proportional is $xy = k$, where $k$ is a constant.
3. In graphing an inverse proportion, you get a hyperbola.
4. Inversely proportional relationships can be represented as $y = \frac{k}{x}$.
5. If the constant $k$ is positive, both variables will either be positive or negative together.

Review Questions

• What happens to one variable when the other variable in an inversely proportional relationship triples?
• How do you express an inversely proportional relationship mathematically?
• What type of graph represents an inverse proportion?

Related terms

Directly Proportional: Two quantities are directly proportional if they increase or decrease at the same rate. This relationship can be represented as $y = kx$.

Constant of Proportionality: A constant value ($k$) that relates two variables in a proportional relationship. It remains unchanged regardless of how the variables change.

Hyperbola: A type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. Inverse proportions graph to form hyperbolas.