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: 29

Answer

$3x+2y=0$

Work Step by Step

Parallel lines have equal slopes. The given line has a slope of $-\frac{3}{2}$. This means that the slope of the line parallel to it is also $-\frac{3}{2}$. Thus, the tentative equation of the line is $y=-\frac{3}{2}x+b$. To find the value of $b$, substitute the x and y-coordinates of $(-4, 6)$ into the tentative equation to have: $y=-\frac{3}{2}x+b \\6 = -\frac{3}{2}(-4)+b \\6 = 6 + b \\6-6=b \\0=b$ Thus, the equation of the line parallel to the given line is $y=-\frac{3}{2}{x}$. Convert this equation to $ax+by=c$ form to have: $y=-\frac{3}{2}x \\\frac{3}{2}x+y=0 \\2(\frac{3}{2}x+y)=0(2) \\3x+2y=0$
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