\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Where:
- \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of two points on the line.
Here's a step-by-step guide on how to find the slope of a line:
1. **Identify Two Points**: Choose any two points on the line. You'll need the coordinates of these points to calculate the slope.
2. **Assign Coordinates**: Label one point as \( (x_1, y_1) \) and the other point as \( (x_2, y_2) \).
3. **Plug Coordinates into the Slope Formula**: Substitute the coordinates of the two points into the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
4. **Calculate the Slope**: Subtract the \( y \)-coordinates of the two points (the rise) and divide by the difference in their \( x \)-coordinates (the run).
5. **Interpret the Slope**: The resulting value is the slope of the line. A positive slope indicates that the line is rising from left to right, while a negative slope indicates that the line is falling from left to right. The magnitude of the slope represents the steepness of the line: a larger slope value indicates a steeper line.
For example, let's say you have two points \( (2, 4) \) and \( (5, 10) \) on a line. To find the slope, you would use these coordinates in the slope formula:
\[ m = \frac{10 - 4}{5 - 2} \]
\[ m = \frac{6}{3} = 2 \]
So, the slope of the line passing through these two points is \( 2 \). This means that for every unit increase in \( x \), the corresponding \( y \) value increases by 2 units.