If y is inversely proportional to x, which equation represents this relationship?

When a variable ( y ) is said to be inversely proportional to another variable ( x ), it means that as ( x ) increases, ( y ) decreases in such a way that their product remains constant. This relationship can be expressed mathematically as ( y = \frac{k}{x} ), where ( k ) is a constant.

In this equation, if ( x ) takes on larger values, ( y ) must take on smaller values to ensure that the product ( y \times x ) equals the constant ( k ). Conversely, if ( x ) is smaller, ( y ) will be larger, maintaining that constant product. Thus, the equation ( y = \frac{k}{x} ) precisely captures the essence of inverse proportionality between ( y ) and ( x ).

The other forms provided in the choices do not accurately represent inverse relationships. For instance, the equation ( y = k + x ) suggests a direct addition rather than an inverse association, while ( y = kx ) indicates direct proportionality. The equation ( y = \frac{x}{k} ) would imply that ( y ) is directly proportional to ( x )