Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Appendix B - Coordinate Geometry and Lines - B Exercises - Page A15: 34


$y= -\frac23x + 6$

Work Step by Step

We are told to find the equation of the line that satisfies the following conditions: $y$-intercept is 6, and parallel to the line $2x + 3y +4 = 0$ To find the equation of the line we must find the slope then write it in the form:$ y =mx + b$ First solve the given equation for $y$: $2x + 3y + 4 = 0$ $3y = -2x - 4$ $y = -\frac{2}{3}x - \frac{4}{3}$ Since the lines are parallel they have the same slope, so the slope of our equation is $m = -\frac23$ $b = 6$ $y = -\frac23x + 6 $
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