What does the equation y = K/x indicate about y and x?

The equation ( y = \frac{K}{x} ) indicates that ( y ) is inversely proportional to ( x ). In this relationship, as the value of ( x ) increases, the value of ( y ) decreases, and vice versa. This inverse relationship stems from the fact that ( K ) is a constant; when ( x ) is multiplied by a factor, ( y ) must decrease proportionally to maintain the equality dictated by the equation.

For example, if you were to double the value of ( x ), ( y ) would be halved in order for the product ( K ) to remain constant. This is the essence of inverse proportionality, where the two variables move in opposite directions in relation to one another.

In contrast, the other provided options don't accurately describe the relationship indicated by the equation. Direct variation describes a scenario where both variables increase or decrease together, which does not apply here. Joint variation would involve another variable that affects ( y ) directly when combined with ( x ), but that is not relevant in this equation either. Lastly, independence suggests that ( y ) does not change at all with changes in ( x), which is