Varies inversely

Definition

Two variables are said to vary inversely if their product is constant. When one variable increases, the other decreases proportionally.

5 Must Know Facts For Your Next Test

1. The general form of an inverse variation is $y = \frac{k}{x}$, where $k$ is a non-zero constant.
2. If $y$ varies inversely as $x$, then $xy = k$, which remains constant.
3. Inverse variation graphs are hyperbolas, not straight lines.
4. In practical problems, inverse variation can model relationships like speed and travel time or intensity of light and distance.
5. To solve inverse variation problems, you often need to find the constant $k$ first using initial conditions.

Review Questions

• What is the general form of an inverse variation equation?
• How does the graph of an inverse variation relationship typically look?
• If $y$ varies inversely as $x$ and when $x = 4$, $y = 3$, what is the value of the constant $k$?

Related terms

Direct Variation:

A relationship where two variables change at a constant rate; represented by the equation $y = kx$.

Constant of Proportionality: The constant value ($k$) that relates two variables in both direct and inverse variations.

Hyperbola:

A type of curve on a graph associated with inverse variations, characterized by its two branches.