## 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 - Page 210: 76

#### Answer

The graphs are not perpendicular.

#### 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: $2x-5y=-3 2x-5y+5y+3=-3+5y+3 \\2x+3=5y \\\frac{2x+3}{5}=\frac{5y}{5} \\\frac{2}{5}x+\frac{3}{5}=y \\y=\frac{2}{5}x+\frac{3}{5}$ Second Equation: $2x+5y=4 \\2x+5y-2x=4-2x \\5y=4-2x \\5y=-2x+4 \\\frac{5y}{5}=\frac{-2x+4}{5} \\y=-\frac{2}{5}x+\frac{4}{5}$ Note that equations have the slopes $\frac{2}{5}$ and $-\frac{2}{5}$. Since $\frac{2}{5} \cdot (-\frac{2}{5}) \ne -1$, then the graphs of the two equations are NOT perpendicular lines.

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