## Calculus 10th Edition

X is multiplied by the constant a. The rate of change in y with respect to x, or $\frac{dy}{dx}$, is therefore a. To produce each y-value, you multiply each x-value by a constant. Therefore, if x changes at a constant rate, so does y. If the constant a is 1, then they change at the same rate. If the constant is anything else, they change at different rates.