What represents an indirect variation relationship in mathematics?

In mathematics, an indirect variation relationship demonstrates that as one variable increases, the other variable decreases, and vice versa. This relationship can be expressed mathematically using the formula x = k/y, where k is a constant.

This formula indicates that for a fixed value of k, if y increases, then x must decrease to keep the product ky constant. This inverse proportion reflects the essence of indirect variation; the two variables are related in such a way that the product of the two remains constant.

The correct representation of indirect variation is pivotal for understanding relationships in various mathematical contexts, including physics and economics, where resources may be considered to have limited availability. Recognizing this foundational concept allows students to apply indirect variation in real-world scenarios effectively.

Other forms, such as y = k/x and x = k/y, also imply an inverse relationship but are commonly used in different contexts or may represent direct relationships depending on how they are interpreted. The key characteristic of an inverse variation is captured accurately in the choice you selected.