Calculus 10th Edition

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

Chapter P - P.2 - Linear Models and Rates of Change - Exercises - Page 17: 46


$y=(-\frac{8}{3})x + (\frac{37}{12})$

Work Step by Step

First find the slope using the two given points. $(\frac{7}{8},\frac{3}{4})(\frac{5}{4},-\frac{1}{4})$ To find the slope use the slope formula $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{(-\frac{1}{4}) – (\frac{3}{4})}{(\frac{5}{4}) – (\frac{7}{8})} = -\frac{1}{\frac{3}{8}} = (-\frac{8}{3})$ Use point slope form to find the equation of the line. $y - y_{1} = m(x - x_{1})$ Note: $x_{2}$ and $y_{2}$ can also be used to solve this equation. $y - (-\frac{1}{4}) = (-\frac{8}{3})(x + \frac{5}{4})$ $y = (-\frac{8}{3})x -(\frac{40}{12}) - (\frac{1}{4})$ Simplify: $y = (\frac{-8}{3})x + (\frac{37}{12})$
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