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: 111

Answer

Points A, B, and C are collinear.

Work Step by Step

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 $A(1,-2)$ and $B(3,-1)$: $slope=\frac{-1-(-2)}{3-1}=\frac{1}{2}$ Next, we calculate the slope between the points $B(3,-1)$ and $C(5,0)$: $slope=\frac{0-(-1)}{5-3}=\frac{1}{2}$ Finally, we calculate the slope between the points $A(1,-2)$ and $C(5,0)$: $slope=\frac{0-(-2)}{5-1}=\frac{2}{4}=\frac{1}{2}$ Since the three slopes are the same, the three points A, B, and C must be collinear.
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