key term - Constant of variation

Definition

The constant of variation is a fixed number that relates two variables which are directly or inversely proportional. It is represented by the symbol $k$ in equations like $y = kx$ (direct variation) and $xy = k$ (inverse variation).

5 Must Know Facts For Your Next Test

1. The constant of variation determines the strength and direction of the relationship between variables.
2. In direct variation, as one variable increases, the other also increases proportionally.
3. In inverse variation, as one variable increases, the other decreases proportionally.
4. The value of the constant of variation can be found by dividing one variable by another in direct variation or multiplying them in inverse variation.
5. Understanding how to manipulate and solve for $k$ is crucial for modeling real-world scenarios using algebraic equations.

Review Questions

Related terms

Direct Variation:

A relationship where one variable is equal to a constant times another variable ($y = kx$).

Inverse Variation:

A relationship where one variable multiplied by another equals a constant ($xy = k$).

Proportionality Constant: Another term for the constant of variation; it represents the factor that relates two proportional quantities.