Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 1 - Linear Functions - 1.1 Slopes and Equations of Lines - 1.1 Exercises: 30

Answer

$2x-y=9$

Work Step by Step

Parallel lines have equal slopes. The given line has a slope of $2$. This means that the slope of the line parallel to it is also $2$. Thus, the tentative equation of the line is $y=2x+b$. To find the value of $b$, substitute the x and y-coordinates of $(2, -5)$ into the tentative equation to have: $y=2x+b \\-5 = 2(2)+b \\-5=4+ b \\-5-4=b \\-9=b$ Thus, the equation of the line parallel to the given line is $y=2x-9$. Convert this equation to $ax+by=c$ form to have: $y=2x-9 \\-2x+y=-9 \\-1(-2x+y)=-9(-1) \\2x-y=9$
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