Key Equations

Direct variation	[latex]y=k{x}^{n},k\text{ is a nonzero constant}[/latex].
Inverse variation	[latex]y=\frac{k}{{x}^{n}},k\text{ is a nonzero constant}[/latex].

Key Concepts

A relationship where one quantity is a constant multiplied by another quantity is called direct variation.
Two variables that are directly proportional to one another will have a constant ratio.
A relationship where one quantity is a constant divided by another quantity is called inverse variation.
Two variables that are inversely proportional to one another will have a constant multiple.
In many problems, a variable varies directly or inversely with multiple variables. We call this type of relationship joint variation.

constant of variation: the non-zero value k that helps define the relationship between variables in direct or inverse variation

direct variation: the relationship between two variables that are a constant multiple of each other; as one quantity increases, so does the other

inverse variation: the relationship between two variables in which the product of the variables is a constant

inversely proportional: a relationship where one quantity is a constant divided by the other quantity; as one quantity increases, the other decreases

joint variation: a relationship where a variable varies directly or inversely with multiple variables

varies directly: a relationship where one quantity is a constant multiplied by the other quantity

varies inversely: a relationship where one quantity is a constant divided by the other quantity