Joint variation

Definition

Joint variation occurs when a variable is directly proportional to the product of two or more other variables. It can be represented by the equation $z = kxy$ where $k$ is a constant.

5 Must Know Facts For Your Next Test

1. In joint variation, if one variable changes, the dependent variable changes in proportion to the product of all independent variables.
2. The constant of variation ($k$) remains unchanged as long as the relationship between variables stays consistent.
3. $z = kxy$ describes a situation where $z$ varies jointly with $x$ and $y$, which means both $x$ and $y$ contribute equally to changes in $z$.
4. Solving for the constant of variation typically requires substituting known values into the joint variation formula.
5. Graphical representations of joint variation often involve three-dimensional plots or contour diagrams to illustrate how changes in two variables affect a third.

Review Questions

• How does changing one independent variable in a joint variation relationship affect the dependent variable?
• Explain how you would determine the constant of variation from given values of $x$, $y$, and $z$.
• What does it mean for a variable to vary jointly with other variables?

Related terms

Direct Variation: A relationship where one variable is directly proportional to another, expressed as $y = kx$ where $k$ is a constant.

Inverse Variation: A relationship where one variable is inversely proportional to another, expressed as $y = \frac{k}{x}$ where $k$ is a constant.

Constant of Variation: The non-zero constant ($k$) that relates two or more variables in direct, inverse, or joint variation scenarios.