What does inverse variation describe?

Inverse variation describes a relationship between two variables where, as one variable increases, the other decreases. This means that the two variables move in opposite directions. For instance, if you have a fixed product of two variables, say ( x ) and ( y ), that product is constant; if ( x ) increases in value, ( y ) must decrease in order to keep the product the same. This relationship can often be expressed mathematically as ( x \times y = k ), where ( k ) is a constant.

The choice indicating that the two variables increase together refers to direct variation, which describes a different type of relationship where both variables grow or shrink in the same manner. The description of one variable increasing while the other also increases is another form of direct variation. Lastly, stating that there is no relationship between the variables suggests independence, which does not capture the essence of inverse variation where such a relationship does very much exist, but in a varying manner. Therefore, the correct understanding of inverse variation is encapsulated by the statement that it depicts two variables going in different directions.