## Intermediate Algebra (12th Edition)

Published by Pearson

# Chapter 2 - Section 2.2 - The Slope of a Line - 2.2 Exercises: 83

#### Answer

Neither parallel nor perpendicular.

#### Work Step by Step

We know that two parallel lines have the same slope ($m_1=m_2$). We also know that perpendicular lines have negative reciprocal slopes ($m_1=-\frac{1}{m_2}$). A line in slope-intercept form has the equation: $y=mx+b$ ($m=slope$, $b=y-intercept$) We put the line equations into slope-intercept form: $4x-3y=6$ $-3y=6-4x$ $y=(6-4x)/-3$ $y=-2+\frac{4}{3}x$ $y=\frac{4}{3}x-2$ $3x-4y=2$ $-4y=2-3x$ $y=(2-3x)/-4$ $y=-\frac{1}{2}+\frac{3}{4}x$ $y=\frac{3}{4}x-\frac{1}{2}$ The two slopes ($\displaystyle \frac{3}{4}$ and $\displaystyle \frac{4}{3}$) are reciprocals of each other, but they are not negative reciprocals. Thus the lines are neither parallel nor perpendicular.

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