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.
