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: 78

Answer

The lines are perpendicular to each other.

Work Step by Step

RECALL: (i) Two lines are parallel if they have (a) equal slopes or (b) undefined slopes. (ii) Two lines are perpendicular if they have (a) slopes whose product is −1 or (b) if one has a zero slope and the other has an undefined slope. (iii) The slope-intercept form of a line's equation is $y=mx+b$ where m = slope and b=y-intercept. Write both equations in slope-intercept form to have: Equation 1: $6y-2x=5 \\6y=2x+5 \\y=\dfrac{2x+5}{6} \\y=\dfrac{1}{3}x+\dfrac{5}{6}$ Equation 2: $2y+6x=1 \\2y=-6x+1 \\y=\dfrac{-6x+1}{2} \\y=-3x+\frac{1}{2}$ Product of slopes: $\frac{1}{3}\times-3=1$ The lines have slopes whose product is equal to −1. Thus, the lines are perpendicular to each other.
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