Which of the following statements is true about inverse variation?

In inverse variation, there is a specific relationship between two variables such that when one variable increases, the other variable decreases in a manner that maintains a constant product. This means that if you multiply the two variables together, the product remains unchanged as one variable intensifies and the other diminishes.

For instance, if we express this relationship mathematically as (x \cdot y = k), where (k) is a constant, it defines inverse variation. So, if (x) increases, (y) must decrease to keep the product (k) constant. This demonstrates that the correct statement accurately captures the fundamental characteristic of inverse variation.

The other choices indicate different types of relationships between variables, such as direct variation (where both variables increase together), constant value relationships (where variables remain unchanged), or both variables decreasing together (which does not align with the defined behavior of inverse variation). Thus, the statement about one variable increasing while the other decreases appropriately reflects the nature of inverse variation.