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 - Page 162: 112


Points are not 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 $A(0,6)$ and $B(4,-5)$: $slope=\frac{-5-6}{4-0}=\frac{-11}{4}=-\frac{11}{4}$ Next, we calculate the slope between the points $B(4,-5)$ and $C(-2,12)$: $slope=\displaystyle \frac{12-(-5)}{-2-4}=\frac{17}{-6}=-\frac{17}{6}$ Since the two slopes are not the same, we know that the three points can not be collinear (we do not need to calculate the slope of AC).
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