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
- The constant of variation determines the strength and direction of the relationship between variables.
- In direct variation, as one variable increases, the other also increases proportionally.
- In inverse variation, as one variable increases, the other decreases proportionally.
- 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.
- Understanding how to manipulate and solve for $k$ is crucial for modeling real-world scenarios using algebraic equations.
Review Questions
- What is the equation form for direct variation and what does the constant of variation represent in this context?
- How do you determine if two variables vary inversely given a set of data points?
- If given an equation $y = 3x$, what is the constant of variation?
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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.
