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

Published by Pearson

# Chapter 3 - Introduction to Graphing - 3.6 Slope-Intercept Form - 3.6 Exercise Set: 75

#### Answer

The graphs are perpendicular lines.

#### Work Step by Step

RECALL: (1) In the slope-intercept form of a line's equation $y=mx+b$, $m$=slope and $b$ is the y-coordinate of the y-intercept. (2) Perpendicular lines have slopes whose product is $-1$ (or negative reciprocals of each other). Write both equations in slope-intercept form to obtain: First Equation: $x-2y=3 x-2y+2y-3=3+2y-3 \\x-3=2y \\\frac{x-3}{2}=\frac{2y}{2} \\\frac{1}{2}x-\frac{3}{2}=y \\y=\frac{1}{2}x-\frac{3}{2}$ Second Equation: $4x+2y=1 \\4x+2y-4x=1-4x \\2y=1-4x \\2y=-4x+1 \\\frac{2y}{2}=\frac{-4x+1}{2} \\y=-2x +\frac{1}{2}$ Note that two equations have the slopes $\frac{1}{2}$ and $-2$. Since $\frac{1}{2} \cdot (-2) = -1$, then the graphs of the two equations are perpendicular lines.

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