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

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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