Elementary Technical Mathematics

Published by Brooks Cole
ISBN 10: 1285199197
ISBN 13: 978-1-28519-919-1

Chapter 8 - Section 8.4 - The Equation of a Line - Exercises - Page 315: 52

Answer

$y=\frac{2}{3}x-\frac{1}{3}$

Work Step by Step

First, we find the slope as follows $$ m=\frac{y_2-y_1}{x_2-x_1}=\frac{1-5}{2-8}=\frac{4}{6}=\frac{2}{3} .$$ The point-slope form of a line is given as: $$y-y_1=m(x-x_1)$$ We plug in the given point and slope and solve for $y$: $$y-1=\frac{2}{3}(x-2)\Longrightarrow y=\frac{2}{3}x-\frac{4}{3}+1=\frac{2}{3}x-\frac{1}{3} .$$
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