## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson

# Chapter 3 - Introduction to Graphing - Test: Chapter 3 - Page 227: 24

#### Answer

The two lines are perpendicular to each other.

#### Work Step by Step

RECALL: (1) The slope-intercept form of a line's equation is $y=mx+b$ where $m$= slope and $(0, b)$ is the line's y-intercept. (2) Parallel lines have the same slope. (3) Perpendicular lines have slopes whose product is $-1$ (negative reciprocals of each other). Write each equation in slope-intercept form by solving for $y$ to obtain: First Equation: $y=-2x+5$ The slope of this line is $-2$. Second Equation: $2y-x=6 \\2y-x+x=6+x \\2y=6+x \\2y=x+6 \\\frac{2y}{2}=\frac{x+6}{2} \\y=\frac{1}{2}x+3$ The slope of this line is $\frac{1}{2}$. Note that $(-2)(\frac{1}{2})=-1$. Thus, the two lines are perpendicular to each other.

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