# Inverse variation

Inverse variation refers to a relationship between two variables where when one variable increases, the other decreases by the same factor. The relationship between the two variables can be modeled by the equation y = , where k is a constant of proportionality. The product of x and y will always equal k.

Inverse variation does not mean that when one variable increases, the other decreases. In order to maintain the same value of k, the value of x cannot be negative when y is positive.

Example

In the table below, x is the number of people in the group, and y is the time required to complete the assignment.

Emma is working on a group assignment with her classmates. Working by herself, the task would take 5 minutes to complete. As she adds more people to her group, the time required to complete the assignment decreases by a factor corresponding to the number of people in the group. Specifically, the time required to complete the assignment alone (5 minutes) is divided by the number of people. In other words, the time it takes for the group to complete the assignment varies inversely with the number of people in the group.

When someone says that y varies inversely with x, or that y is inversely proportional to x, they mean that y and x exhibit inverse variation.

See also constant of proportionality.