Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.10 - Lines - 1.10 Exercises - Page 115: 50

Answer

$y=2x-7$, or, in general form, $2x-y-7=0$

Work Step by Step

Through $(-2,-11);$ perpendicular to the line passing through $(1,1)$ and $(5,-1)$ A point through which the line passes and the fact that the line whose equation must be found is perpendicular to the line passing through $(1,1)$ and $(5,-1)$ are known. Use the point-slope form of the equation of a line, which is $y-y_{1}=m(x-x_{1})$, where $(x_{1},y_{1})$ is a point through which the line passes and $m$ is the slope. Two points through which the line perpendicular to the one whose equation must be found passes are known. Use them to find its slope: $m_{\perp}=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}=\dfrac{-1-1}{5-1}=\dfrac{-2}{4}=-\dfrac{1}{2}$ The slopes of perpendicular lines are negative reciprocals, so the slope of the line whose equation must be found is: $m=-\dfrac{1}{\Big(-\dfrac{1}{2}\Big)}=2$ Substitute $(x_{1},y_{1})$ and $m$ into the point-slope form of the equation of a line formula and simplify to obtain the answer: $y-y_{1}=m(x-x_{1})$ $y+11=2(x+2)$ $y+11=2x+4$ $y=2x+4-11$ $y=2x-7$, or, in general form, $2x-y-7=0$
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