Question

How to check the run of a slope

Answer 1

In mathematics, particularly in the context of linear equations and geometry, the "run" refers to the horizontal change between two points on a line, while "rise" refers to the vertical change. The slope of a line is often described in terms of rise over run, typically represented as \(\frac{\text{rise}}{\text{run}}\).

To check the run of a slope, follow these steps:

1. **Identify Two Points on the Line**: You need two points on the line, which can be expressed as coordinates \((x_1, y_1)\) and \((x_2, y_2)\).

2. **Calculate the Run**: The run can be found by calculating the difference between the x-coordinates of the two points:

\[
\text{Run} = x_2 - x_1
\]

3. **Ensure the Run is Not Zero**: If the run equals zero, that means the line is vertical and the slope is undefined. In such cases, the slope formula won't apply.

4. **Calculate the Slope (if needed)**: If you want to find the slope, you can use both rise and run:

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

### Example
Suppose you have two points: A(2, 3) and B(5, 7).

1. Identify the coordinates:
- Point A: \((2, 3)\)
- Point B: \((5, 7)\)

2. Calculate the run:
\[
\text{Run} = 5 - 2 = 3
\]

3. Calculate the rise (optional):
\[
\text{Rise} = 7 - 3 = 4
\]

4. Calculate the slope (for reference):
\[
\text{Slope} (m) = \frac{4}{3}
\]

Using these steps, you can adequately check the run of a slope and determine the characteristics of the line it represents.