Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.1 Parametric Equations - Exercises - Page 604: 50


$$ \frac{d y}{d x} =\frac{7}{2} $$ and at $t=1$, we have $$ \frac{d y}{d x}= \frac{7}{2}. $$

Work Step by Step

Since $x=2t+9$ and $y=7t-9$ then we have $$ \frac{d y}{d x}=\frac{d y / d t}{d x / d t}=\frac{y^{\prime}(t)}{x^{\prime}(t)}=\frac{7}{2}= $$ and at $t=1$, we have $$ \frac{d y}{d x}= \frac{7}{2}. $$
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