Which formula represents an inverse variation?

An inverse variation is characterized by the relationship where one variable increases while the other variable decreases, maintaining a constant product. This relationship can be mathematically represented by the formula ( y = \frac{k}{x} ), where ( k ) is a non-zero constant.

In this formula, as the value of ( x ) increases, the value of ( y ) decreases in such a way that the product ( xy = k ) remains consistent. This clearly illustrates the concept of inverse variation, highlighting how the two variables are reciprocally related.

The other choices given do not represent inverse variations. For instance, in ( y = kx ), both ( y ) and ( x ) increase together if ( k ) is a positive constant, indicating a direct variation instead. The form ( y = x^2 ) suggests that as ( x ) increases, ( y ) also increases at an increasing rate, again indicating direct variation. Lastly, the expression ( y = x + k ) represents a linear relationship where both ( y ) and ( x ) move together positively.

Therefore, the appropriate formula representing an inverse variation is indeed ( y = \frac{k}{x} ).