# Summary: Variation

## Key Equations

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

Inverse variation | [latex]y=\dfrac{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.

## Glossary

**constant of variation**- the non-zero value [latex]k[/latex] 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

## Licenses & Attributions

### CC licensed content, Original

- Revision and Adaptation.
**Provided by:**Lumen Learning**License:**CC BY: Attribution.

### CC licensed content, Shared previously

- Precalculus.
**Provided by:**OpenStax**Authored by:**Jay Abramson, et al..**Located at:**https://openstax.org/books/precalculus/pages/1-introduction-to-functions.**License:**CC BY: Attribution.**License terms:**Download For Free at : http://cnx.org/contents/[email protected].. - College Algebra.
**Provided by:**OpenStax**Authored by:**Abramson, Jay et al..**License:**CC BY: Attribution.**License terms:**Download for free at http://cnx.org/contents/[email protected].