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

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 3 - Introduction to Graphing - Review Exercises: Chapter 3 - Page 226: 49


The lines are parallel to each other.

Work Step by Step

RECALL: (1) Parallel lines have the same slope. (2) Perpendicular lines have slopes whose product is $-1$ (negative reciprocals of each other). (3) 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. Write both equations in slope-intercept form to obtain: First Equation: $3x-5=7y \\\frac{3x-5}{7}=\frac{7y}{7} \\\frac{3}{7}x-\frac{5}{7}=y \\y=\frac{3}{7}x-\frac{5}{7}$ The slope of this line is $\frac{3}{7}$. Second Equation: $7y-3x=7 \\7y-3x+3x=7+3x \\7y=7+3x \\7y=3x+7 \\\frac{7y}{7}=\frac{3x+7}{7} \\y=\frac{3}{7}x+1$ The slope of this line is $\frac{3}{7}$. Since the two lines have the same slope, then they are parallel to each other.
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