Step 1 :The problem provides us with two lines, Line 1 and Line 2, and the coordinates of two points on each line.
Step 2 :Line 1 passes through the points (0,9) and (4,-31).
Step 3 :Line 2 passes through the points (-1,16) and (9,-84).
Step 4 :We can find the slope of a line using the formula: \(m = \frac{y_2 - y_1}{x_2 - x_1}\), where (x_1, y_1) and (x_2, y_2) are the coordinates of two points on the line.
Step 5 :Let's use this formula to find the slopes of Line 1 and Line 2.
Step 6 :For Line 1, substituting the given points into the formula, we get: \(m = \frac{-31 - 9}{4 - 0} = -10.0\)
Step 7 :For Line 2, substituting the given points into the formula, we get: \(m = \frac{-84 - 16}{9 - (-1)} = -10.0\)
Step 8 :So, the slopes of Line 1 and Line 2 are both -10.0.
Step 9 :Final Answer: The slopes of Line 1 and Line 2 are both \(\boxed{-10.0}\)