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How Do I Figure Rise Over Run?

Rise over run is both a description and a method of calculating the slope of a line. Slope is the steepness of a graphed line or physical plane. In mathematics, slope also describes the rate of change between two points. The rate of change applies to physical calculations such as acceleration (the rate of change of velocity) and interest accrual (the rate of change in a bank balance), among myriad other uses. Rise over run describes slope because the formula used to determine slope is written as a fraction, with the change in position along the vertical y-axis (rise) above the change in position along the horizontal x-axis (run).

Things You'll Need

  • Graph paper
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Instructions

    • 1

      Select two points on a graphed line between which you wish to determine the slope. Record the coordinates for each point in the (x, y) format on a slip of scratch paper. Write the position of each point along the horizontal axis first, followed by the position of each point along the vertical axis.

    • 2

      Calculate the change in y. Subtract the second y coordinate from the first y coordinate. Record the result in the numerator section of the slope formula (the part above the line).

    • 3

      Calculate the change in x. Subtract the second x coordinate from the first x coordinate. Record the result in the denominator section of the slope formula (the part below the line). The resulting fraction is one way of representing the slope (rise over run). To represent the slope as a decimal instead, divide the denominator (the run, or change in x) into the numerator (the rise, or change in y).

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