What equation represents inverse variation?

Inverse variation describes a relationship between two variables in which the product of the two variables is a constant. In mathematical terms, if y varies inversely with x, then we can express this relationship using the equation y = k/x, where k is a non-zero constant. This means that as one variable increases, the other decreases, maintaining the product (k) constant.

The equation y = k/x clearly indicates this relationship, as multiplying both y and x would yield the constant k. For instance, if x is doubled, y must be halved to keep their product equal to k. This behavior is characteristic of inverse variation, distinguishing it from other types of relationships such as direct variation where an increase in one variable leads to a proportional increase in another.

In contrast, other given equations such as y = kx represent direct variation, where both variables move in the same direction, while y = x^2 and y = ax + b represent polynomial and linear relationships respectively, which also do not depict inverse variation.