Step 1 :The problem is asking for the slope of the line that contains the points $(2,-7)$ and $(-1,5)$.
Step 2 :The slope of a line that passes through two points $(x_1, y_1)$ and $(x_2, y_2)$ can be calculated using the formula: \( m = \frac{y_2 - y_1}{x_2 - x_1} \)
Step 3 :Substitute the given points into the formula: \( m = \frac{5 - (-7)}{-1 - 2} \)
Step 4 :Simplify the equation to find the slope: \( m = -4.0 \)
Step 5 :Final Answer: The slope of the line that contains the points $(2,-7)$ and $(-1,5)$ is \(\boxed{-4}\)