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To find the slope of a line, you need to know the coordinates of two points on the line. Once you have the coordinates of the points, you can use the slope formula. The slope (\(m\)) represents the rate at which the line rises or falls as you move from left to right along the line. Here's the slope formula:

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\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]


- \( (x_1, y_1) \) 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.
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