What does "xy=k" indicate about the relationship between x and y?

• A. They vary directly
• B. They are independent
• C. They vary inversely
• D. They are equal

Answer: (C)

The equation ( xy = k ) indicates an inverse variation between the variables ( x ) and ( y ). This relationship means that as one variable increases, the other must decrease to keep the product ( k ) constant. In this context, if you solve for ( y ), you get ( y = \frac{k}{x} ). Here, ( k ) is a constant, which reinforces the idea that any increase in ( x ) would lead to a proportional decrease in ( y ), and vice versa, maintaining the equality ( k ) throughout.

Thus, the correct answer highlights that ( x ) and ( y ) do not change independently of each other; instead, they have a specific dependent relationship that defines how one affects the other through multiplication to reach the constant value ( k ).