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: 25



Work Step by Step

First, we find the slope. To find the slope of the line passing through $(2,1)$ and $(1,6)$, we use the slope formula: $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$. Plug in the given values of $x$ and $y$: $m=\frac{6-1}{1-2}$. Simplify to arrive at the slope: $m=-{5}$. We plug in the slope and the values of $x$ and $y$ into the equation $y=mx+b$: $1=-5(2)+b$. Solve for $b$: $1=b-10$ $b=11$. Plug in the values of $m$ and $b$ into the formula to find the equation of the line: $y=-5x+11$.
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