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 163: 22


$ y+8=\displaystyle \frac{5}{4}(x-4) \qquad$ ... point-slope form $y=\displaystyle \frac{5}{4}x-13 \qquad$ ... slope-intercept form $f(x)=\displaystyle \frac{5}{4}x-13$ $\qquad$ ... function notation

Work Step by Step

$(x_{1},y_{1})=(4,-8),\ \; (x_{2},y_{2})=(8,-3)$ $m=\displaystyle \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-3-(-8)}{8-4}=\frac{5}{4}$. So with $m=\displaystyle \frac{5}{4}$ and $(x_{1},y_{1})=(4,-8)$, we write the point-slope form $y-y_{1}=m(x-x_{1})$ $ y+8=\displaystyle \frac{5}{4}(x-4) \qquad$ ... point-slope form Simplify to slope-intercept form, $ y=mx+b$ ... distribute $ y+8=\displaystyle \frac{5}{4}x-5 \qquad$ ...add $(-8)$ $ y=\displaystyle \frac{5}{4}x-13 \qquad$ ... is the slope-intercept form For function notation, replace $y$ with $f(x)$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.