Which expression describes inverse variation between two quantities?

Which expression describes inverse variation between two quantities?

• A. y = kx
• B. y = x - k
• C. y = k/x
• D. y = x^2

Answer: (C)

Inverse variation means two quantities move in opposite directions so that their product stays constant. The expression y = k/x embodies this idea: as x gets larger, y gets smaller in such a way that xy remains equal to the constant k. This constant-product relationship is the defining feature of inverse variation. The other forms describe different relationships. y = kx is direct variation—y grows linearly with x. y = x - k is a linear relationship with a shift, not an inverse variation. y = x^2 is a quadratic relationship, where y grows with the square of x, not inversely. So y = k/x is the expression that best captures inverse variation.

Inverse variation means two quantities move in opposite directions so that their product stays constant. The expression y = k/x embodies this idea: as x gets larger, y gets smaller in such a way that xy remains equal to the constant k. This constant-product relationship is the defining feature of inverse variation.

The other forms describe different relationships. y = kx is direct variation—y grows linearly with x. y = x - k is a linear relationship with a shift, not an inverse variation. y = x^2 is a quadratic relationship, where y grows with the square of x, not inversely. So y = k/x is the expression that best captures inverse variation.