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 the product remains unchanged.

5 Must Know Facts For Your Next Test

1. In an inverse proportion, if $x$ and $y$ are the two quantities, then $x \cdot y = k$, where $k$ is a constant.
2. The graph of an inversely proportional relationship is a hyperbola.
3. If $y$ is inversely proportional to $x$, then $y = \frac{k}{x}$ for some constant $k$.
4. As one variable approaches zero, the other variable approaches infinity (and vice versa).
5. Inverse proportionality can be applied to modeling real-world scenarios like speed and travel time at a constant distance.

Review Questions

• What is the general form of an equation representing two inversely proportional quantities?
• How does the graph of an inversely proportional relationship look?
• If $x \cdot y = 12$, what is y when x = 3?

Related terms

Directly Proportional: Two quantities are directly proportional if their ratio is constant; when one increases, so does the other.

Constant of Proportionality: The constant value ($k$) in the relationship between two directly or inversely proportional quantities.

Hyperbola: A type of smooth curve lying in a plane, defined by its geometric properties or by equations that describe it as an inverse relation.