Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

APPENDIX B - Coordinate Geometry and Lines - B Exercises - Page A 15: 23



Work Step by Step

To find an equation of a line with slope $m=\frac{2}{3}$ that passes through $(1,7)$, we use the formula $y=mx+b$. We plug in the values of $m$, $y$, and $x$ to solve for $b$: $7=\frac{2}{3}(1)+b$. Solve for $b$: $b+\frac{2}{3}=7$ $b=\frac{19}{3}$. Plug values of $m$ and $b$ into the formula to get the equation of the line: $y=\frac{2}{3}x+\frac{19}{3}$. Multiply by 3 on both sides to simplify: $3y=2x+19$.
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