University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 10 - Section 10.1 - Parametrizations of Plane Curves - Exercises - Page 563: 22


$x=t$ and $y=-\dfrac{5}{4}t+\dfrac{7}{4}$ and $-1\leq t \leq 3$ (Other answers are possible.)

Work Step by Step

The slope of a line between two points can be found as: $m=\dfrac{-2-3}{3-(-1)}=-\dfrac{5}{4}$ Now, $y-y_0=m(x-x_0) \implies y-(-2)=-\dfrac{5}{4}(x-3)$ This implies that $y=-\dfrac{5}{4}x+\dfrac{7}{4}$ Consider $x=t$ Then $y=-\dfrac{5}{4}t+\dfrac{7}{4}$ and $-1\leq t \leq 3$
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