Which expression represents a direct variation between y and x?

The expression that represents a direct variation between ( y ) and ( x ) is one where ( y ) is directly proportional to ( x ). This means that as ( x ) increases or decreases, ( y ) will increase or decrease by a constant multiple, denoted by ( k ). The relationship can be represented by the equation ( y = Kx ), where ( K ) is a nonzero constant.

In this equation, if you multiply ( x ) by a certain factor (whether it's positive or negative), the value of ( y ) will change by the same factor multiplied by ( K ). Thus, this form confirms that ( y ) varies directly with ( x ).

The other forms, while they might represent other types of relationships, do not maintain this direct variation. The expression ( y = K/x ) represents an inverse variation, where ( y ) decreases as ( x ) increases. The expression ( y = kxz ) suggests a multi-variable relationship and does not imply a direct one-to-one variation with ( x ) alone. Finally, ( y = K + x ) indicates a linear relationship that does not represent direct variation, as the