Inverse variations

Definition

Inverse variations describe a relationship between two variables where the product of the variables is constant. It is typically expressed as $y = \frac{k}{x}$ or $xy = k$, where $k$ is a non-zero constant.

5 Must Know Facts For Your Next Test

1. In an inverse variation, as one variable increases, the other decreases and vice versa.
2. The graph of an inverse variation is a hyperbola.
3. If $xy = k$, then $k$ must be a non-zero constant for the relationship to hold.
4. Inverse variations can model real-world scenarios like speed and travel time or supply and demand relationships.
5. To solve problems involving inverse variations, identify the constant $k$ first by using given values.

Review Questions

• What does the equation $xy = k$ represent in terms of inverse variation?
• Explain how the graph of an inverse variation function looks like.
• How do you determine the constant of variation in an inverse variation problem?

Related terms

Direct Variation: A relationship where one variable is a constant multiple of another, expressed as $y = kx$.

Hyperbola: A type of smooth curve lying in a plane, defined by its geometric properties or equations that describe it as a conic section.

Constant of Variation: $k$ in both direct and inverse variations; it remains unchanged as the variables change.