The slope of a line is a measure of its steepness and direction. Mathematically, it's defined as the ratio of the change in the vertical direction (rise) to the change in the horizontal direction (run) between two points on the line.

The formula for calculating the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Key Points:

• If the slope is positive, the line rises as it moves from left to right.
• If the slope is negative, the line falls as it moves from left to right.
• A slope of zero indicates a horizontal line.
• An undefined slope (division by zero) indicates a vertical line.

Would you like a more detailed explanation or have any questions?

Here are 5 related questions:

1. How do you find the slope of a line given an equation?
2. What does the slope-intercept form of a line look like?
3. How does the slope relate to parallel and perpendicular lines?
4. Can you explain the concept of the slope in a real-world context?
5. What happens to the slope when the line is vertical or horizontal?

Tip: When working with slopes, always ensure that the difference in the x-values ($x_2 - x_1$) is not zero to avoid undefined results.