Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 5 - Linear Functions - 5-1 Rate of Change and Slope - Practice and Problem-Solving Exercises: 54

Answer

Yes; the slopes between each pair of points are the same, so the points lie on the same line.

Work Step by Step

To find if all the points lie on the same line, the slope between each pair of points must be the same. Use the slope formula: $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ The points are $G(1,-2), H(-1,-5) , I(5,4)$ The slope between $G(1,-2)$ and $H(−1,-5)$ is: $m=\frac{-5-(-2)}{-1-1}$=$\frac{-3}{-2}$=$\frac{3}{2}$ The slope between $H(−1,-5)$ and $I(5,4)$ is: $m=\frac{4-(-5)}{5-(-1)}$=$\frac{9}{6}$=$\frac{3}{2}$ Both slopes are the same, so the points lie on the same line.
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