Which of the following indicates that y varies inversely with x?

The relationship that indicates y varies inversely with x is represented mathematically as y = K/x, where K is a constant. In this equation, as the value of x increases, the value of y decreases, and vice versa. This demonstrates the nature of inverse variation: the product of the two variables (y and x) remains constant (equal to K) as one variable goes up while the other goes down.

In contrast, the other given choices depict different relationships. The first choice, y = kx, suggests a direct variation; as x increases, y also increases. The third choice, y = kxz, suggests that y varies directly with both x and z, meaning y would increase with increases in either variable. The last choice, y = x + z, indicates a simple additive relationship, not a relationship of inverse variation. Thus, the only expression that correctly portrays inverse variation is y = K/x.