The slope of a line describes how steep the line is, representing the change in the vertical direction (rise) relative to the change in the horizontal direction (run). To find the slope of a line, you typically follow these steps:

Formula for the Slope:

The slope (denoted as $m$) between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ This is also expressed as: $\text{slope} = \frac{\text{rise}}{\text{run}}$

Steps to Find the Slope:

1. Identify two points on the line. Each point is represented as $(x_1, y_1)$ and $(x_2, y_2)$.

2. Subtract the y-coordinates ($y_2 - y_1$) to get the rise (vertical change).

3. Subtract the x-coordinates ($x_2 - x_1$) to get the run (horizontal change).

4. Divide the rise by the run to calculate the slope.

Example:

Suppose you have two points $(1, 3)$ and $(4, 11)$. Using the slope formula:

$m = \frac{11 - 3}{4 - 1} = \frac{8}{3}$

So, the slope of the line passing through these points is $\frac{8}{3}$.

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Do you want more details on any part of this?

Here are some related questions:

1. How do you find the slope of a line from a graph?
2. How does the slope formula change for vertical and horizontal lines?
3. Can slope be negative? How do you interpret that?
4. How do you find the slope of a line given its equation?
5. What is the meaning of the slope in real-world situations?

Tip: A positive slope means the line rises as it moves from left to right, while a negative slope means it falls.