Question

rise/run
x
-4,-1,2,5,8

y
4,3,2,1,0

Answer 1

To find the rise/run for the points you provided, we will calculate the slope between each pair of points. The formula for slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[
m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}
\]

Given the points:

- Point 1: \((-4, 4)\)
- Point 2: \((-1, 3)\)
- Point 3: \((2, 2)\)
- Point 4: \((5, 1)\)
- Point 5: \((8, 0)\)

Let's calculate the slope between each consecutive pair of points.

1. Between Point 1 \((-4, 4)\) and Point 2 \((-1, 3)\):
\[
m = \frac{3 - 4}{-1 - (-4)} = \frac{-1}{3} = -\frac{1}{3}
\]

2. Between Point 2 \((-1, 3)\) and Point 3 \((2, 2)\):
\[
m = \frac{2 - 3}{2 - (-1)} = \frac{-1}{3} = -\frac{1}{3}
\]

3. Between Point 3 \((2, 2)\) and Point 4 \((5, 1)\):
\[
m = \frac{1 - 2}{5 - 2} = \frac{-1}{3} = -\frac{1}{3}
\]

4. Between Point 4 \((5, 1)\) and Point 5 \((8, 0)\):
\[
m = \frac{0 - 1}{8 - 5} = \frac{-1}{3} = -\frac{1}{3}
\]

### Summary of Slopes (Rise/Run)
- Between \((-4, 4)\) and \((-1, 3)\): \(-\frac{1}{3}\)
- Between \((-1, 3)\) and \((2, 2)\): \(-\frac{1}{3}\)
- Between \((2, 2)\) and \((5, 1)\): \(-\frac{1}{3}\)
- Between \((5, 1)\) and \((8, 0)\): \(-\frac{1}{3}\)

The rise/run (slope) between each consecutive pair of points is consistently \(-\frac{1}{3}\).