College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.3 - Lines - 1.3 Exercises: 78

Answer

The two lines are perpendicular to each other.

Work Step by Step

RECALL: (1) Parallel lines have equal slopes. (2) Perpendicular lines have slopes whose product is $-1$. (3) The slope-intercept form of a line's equation is $y=mx+b$ where $m$ = slope. Write both equations in slope-intercept form to obtain: $\bf\text{Equation 1}:$ $6y-2x=5 \\6y=2x+5 \\\dfrac{6y}{6} = \dfrac{2x+5}{6} \\y = \dfrac{2}{6}x + \dfrac{5}{6} \\y=\dfrac{1}{3}x+\dfrac{5}{6}$ $\bf\text{Equation 2}:$ $2y+6x=1 \\2y=-6x+1 \\\dfrac{2y}{2} = \dfrac{-6x+1}{2} \\y=-3x+\dfrac{1}{2}$ The two lines have slopes that are negative reciprocals of each other (product is -1). Thus, the two lines are perpendicular to each other.
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