# Key Equations

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

# 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.

## Glossary

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