In Exercises 45–46, describe in words the variation shown by the given equation. z = k√x / y^2

Key Concepts

Direct Variation

Direct variation occurs when one variable is a constant multiple of another. In the context of the equation z = k√x / y², z varies directly with the square root of x, meaning that as x increases, z increases proportionally, provided y remains constant.

Inverse Variation

Inverse variation describes a relationship where one variable increases as another decreases. In this equation, z varies inversely with y², indicating that as y increases, z decreases, assuming x remains constant. This relationship highlights how changes in one variable can affect another in opposite ways.

Constant of Variation

The constant of variation, represented by k in the equation, is a fixed value that determines the strength of the relationship between the variables. It scales the relationship between z, x, and y², indicating how much z changes in response to changes in x and y, thus providing a specific context for the variation described.