\[ m = \frac{y₂ - y₁}{x₂ - x₁} \]

Here's how to calculate the slope of a line:

1. **Identify Two Points**: Choose two points on the line for which you want to calculate the slope. Let's denote them as (x₁, y₁) and (x₂, y₂).

2. **Calculate the Change in Y**: Subtract the y-coordinate of the first point from the y-coordinate of the second point. This gives you the change in y, represented as \( \Delta y \).

\[ \Delta y = y₂ - y₁ \]

3. **Calculate the Change in X**: Subtract the x-coordinate of the first point from the x-coordinate of the second point. This gives you the change in x, represented as \( \Delta x \).

\[ \Delta x = x₂ - x₁ \]

4. **Calculate the Slope**: Divide the change in y by the change in x to find the slope of the line.

\[ m = \frac{\Delta y}{\Delta x} = \frac{y₂ - y₁}{x₂ - x₁} \]

This formula represents the rise-over-run method, where the rise (change in y) is divided by the run (change in x).

5. **Interpret the Slope**: The slope indicates the steepness of the line. A positive slope indicates that the line is increasing from left to right, while a negative slope indicates that the line is decreasing. The magnitude of the slope represents the rate of change: steeper lines have larger slopes.

6. **Special Cases**:

- If the line is vertical (parallel to the y-axis), the slope is undefined because the change in x is zero.

- If the line is horizontal (parallel to the x-axis), the slope is zero because the change in y is zero.

By following these steps, you can calculate the slope of a line passing through two points. This calculation is fundamental in various fields, including mathematics, physics, engineering, and economics.