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: 44

Answer

$y=-\dfrac{2}{3}x+6$, or, in general form, $2x+3y-18=0$

Work Step by Step

$y$-intercept $6;$ parallel to the line $2x+3y+4=0$ Use the slope-intercept form of the equation of a line, which is $y=mx+b$, where $m$ is the slope and $b$ is the $y$-intercept. The $y$-intercept and the equation of a line parallel to the one to be found are given. Solve the given equation for $y$. The resulting expression will be in slope-intercept form and the slope $m$ will be the number in front of $x$: $2x+3y+4=0$ $3y=-2x-4$ $y=-\dfrac{2}{3}x-\dfrac{4}{3}$ The slope of the given line is $-\dfrac{2}{3}$ Since the line whose equation must be found is parallel to the line whose equation is given, then the slope of the first is also $-\dfrac{2}{3}$ Substitute the $y$-intercept given and the slope into the slope-intercept form of the equation of a line formula and simplify to obtain the answer: $y=mx+b$ $y=-\dfrac{2}{3}x+6$, or, in general form, $2x+3y-18=0$
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