Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.6 Exercises: 9

Answer

y does change at a constant rate, but not necessarily the same rate as x.

Work Step by Step

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.
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