Calculus with Applications (10th Edition)

Published by Pearson

Chapter 1 - Linear Functions - 1.1 Slopes and Equations of Lines - 1.1 Exercises: 31

Answer

$x-y=7$

Work Step by Step

Perpendicular lines have slopes that are negative reciprocals of each other. The given line has a slope of $-1$. This means that the slope of the line perpendicular to it is $1$. Thus, the tentative equation of the line is $y=x+b$. To find the value of $b$, substitute the x and y-coordinates of $(3, -4)$ into the tentative equation to have: $y=x+b \\-4 = 3+b \\-4-3= b \\-7=b$ Thus, the equation of the line parallel to the given line is $y=x-7$. Convert this equation to $ax+by=c$ form to have: $y=x-7 \\-x+y=-7 \\-1(-x+y)=-7(-1) \\x-y=7$

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