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  • Understanding Slope: Calculating the Rate of Change in Lines
    The ratio of a vertical change to the corresponding horizontal change in a line is called the slope.

    Here's a breakdown:

    * Vertical Change: This is the difference in the y-coordinates of two points on the line. It's often referred to as the "rise."

    * Horizontal Change: This is the difference in the x-coordinates of the same two points. It's often referred to as the "run."

    Formula for Slope:

    Slope (m) = (change in y) / (change in x) = (rise) / (run)

    Example:

    Let's say you have two points on a line: (2, 1) and (4, 5).

    * Vertical Change (rise): 5 - 1 = 4

    * Horizontal Change (run): 4 - 2 = 2

    Therefore, the slope of the line is 4/2, which simplifies to 2. This means that for every 2 units you move to the right (horizontally), you move 4 units upwards (vertically).

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