Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 2 - Section 2.5 - The Point-Slope Form of the Equation of a Line - Exercise Set - Page 164: 53


$ y-2=\displaystyle \frac{2}{3}(x+2) \qquad$ ... point-slope form $ y=\displaystyle \frac{2}{3}x+\frac{10}{3} \qquad$ ... slope-intercept form

Work Step by Step

The line ... $ 2x-3y=7\qquad$... solve for y $-3y=-2x+7 \qquad$... $/\div(-3)$ $y=\displaystyle \frac{2}{3}x-\frac{7}{3}$ .. is now in slope-intercept form. Its slope is $m=\displaystyle \frac{2}{3}.$ A line parallel to it has the same slope, $m=\displaystyle \frac{2}{3}$ and passes through $(x_{1},y_{1})=(-2,2)$ We write the point-slope equation: $y-y_{1}=m(x-x_{1})$ $ y-2=\displaystyle \frac{2}{3}(x+2) \qquad$ ... point-slope form Simplify to slope-intercept form (solve for y) $ y-2=\displaystyle \frac{2}{3}x+\frac{4}{3} \qquad$ ...add $2$ $ y=\displaystyle \frac{2}{3}x+\frac{10}{3} \qquad$ ... is the slope-intercept form
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