Varies inversely

Definition

Two variables are said to vary inversely if their product is constant. When one variable increases, the other decreases in such a way that the product of the two variables remains unchanged.

5 Must Know Facts For Your Next Test

1. The general form of an inverse variation equation is $xy = k$, where $k$ is a non-zero constant.
2. If $x$ varies inversely as $y$, then $y = \frac{k}{x}$.
3. Inverse variation graphs are hyperbolas that open along the x and y axes.
4. In real-world problems, inverse variation can describe relationships like speed and time for a fixed distance.
5. To determine if two quantities vary inversely, you can check if their product remains constant.

Review Questions

• What is the general form of an inverse variation equation?
• How would you represent an inverse relationship between x and y algebraically?
• What type of graph represents an inverse variation?

Related terms

Direct Variation: A relationship between two variables where one is a constant multiple of the other. Represented by $y = kx$.

Constant of Variation: The fixed value ($k$) in both direct and inverse variation equations.

Hyperbola: A type of curve on a graph that represents the set of all points for which the difference between the distances to two foci is constant, commonly seen in graphs of inverse variations.