Which function has an equation of the form y = ax, where "a" is a non-zero constant?

The function described by the equation y = ax, where "a" is a non-zero constant, represents a direct variation. In this context, direct variation indicates that y varies directly with x, meaning that as x increases or decreases, y will do so proportionally, according to the value of "a."

The constant "a" serves as the constant of proportionality, indicating the rate at which y changes with respect to x. For instance, if a is positive, y increases as x increases; if a is negative, y decreases as x increases. The relationship is linear, and when graphed, it will indeed form a straight line through the origin, reinforcing the linear nature of the equation.

This definition differentiates it from other function types, as inverse variation describes relationships where one variable increases and the other decreases, while quadratic functions involve squared variables leading to parabolic shapes. Thus, stating that the equation is of the form y = ax aligns perfectly with the concept of direct variation.