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 - Page 114: 75


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: $\bf\text{Equation 1}:$ $-3x+4y=4 \\4y=3x+4 \\\dfrac{4y}{4} = \dfrac{3x+4}{4} \\y = \dfrac{3}{4}x + 1$ $\bf\text{Equation 2}:$ $4x+3y=5 \\3y=-4x+5 \\\dfrac{3y}{3} = \dfrac{-4x+5}{3} \\y=-\dfrac{4}{3}x+\dfrac{5}{3}$ 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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