Joint variation

Definition

Joint variation occurs when a variable depends on two or more other variables, typically expressed as a product of those variables multiplied by a constant. It is represented mathematically as $z = k \cdot x \cdot y$ where $k$ is a non-zero constant.

5 Must Know Facts For Your Next Test

1. In joint variation, if one variable increases while the others are held constant, the dependent variable will increase proportionally to that change.
2. The equation for joint variation can be extended to include more variables, such as $z = k \cdot x \cdot y \cdot w$.
3. Solving problems involving joint variation often requires isolating the constant $k$ by using known values of the variables.
4. Joint variation combines aspects of both direct and inverse variations but applies to multiple variables simultaneously.
5. Understanding how to manipulate and solve equations involving joint variation is crucial for modeling real-world scenarios in algebra.

Review Questions

• What is the general form of an equation representing joint variation?
• How does changing one variable in a joint variation equation affect the dependent variable?
• Can you extend the concept of joint variation to include more than two independent variables? Provide an example.

Related terms

Direct Variation:

$y = kx$, where $y$ varies directly as $x$ and $k$ is a non-zero constant.

Inverse Variation:

$y = \frac{k}{x}$, where $y$ varies inversely as $x$ and $k$ is a non-zero constant.

Constant of Variation:

$k$, which represents the proportionality factor in both direct and inverse variations.