Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 2 - Section 2.2 - The Slope of a Line - 2.2 Exercises: 79



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 ($m_1=-\frac{1}{m_2}$). To calculate the slope between points $(x_1,y_1)$ and $(x_2,y_2)$, we use the formula: $slope=m=\frac{y_2-y_1}{x_2-x_1}$ We calculate the slope between the points $(15,\ 9)$ and $(12,\ -7)$: $slope=m=\displaystyle \frac{-7-9}{12-15}=\frac{-16}{-3}=\frac{16}{3}$ Next, we calculate the slope between the points $(8,\ -4)$ and $(5,\ -20)$: $slope=m=\displaystyle \frac{-20-(-4)}{5-8}=\frac{-16}{-3}=\frac{16}{3}$ We see that the slopes are equal. Thus the lines are parallel.
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