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
