How Do You Find the Slope With Two Points?


Quick Answer

To find the slope of a line, you need the ratio of the change in y to the change in x. Even if there is no equation, you can still derive the slope by comparing two points on the line. After doing this, you can extrapolate the intercepts.

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Full Answer

  1. Determine the two points to be used

    These points are written as ordered pairs (x, y). The first number is the x-coordinate, and the second is the y-coordinate. Rearrange them with the largest x-value first, because this makes it easier to calculate the slope.

  2. Subtract the y-values and the x-values

    For example, assume you have two ordered pairs (2, 5) and (6, 1). You subtract 5 from 1, revealing -4 for the change in y. Subtracting 2 from 6 yields 4 for the change in x.

  3. Express the number as a ratio

    Slope is the ratio of rise to run, or y to x. Therefore, in the example equation it is -4/4. Simplified, the line represented by the two ordered pairs has a slope of -1. By writing the line's equation in the form of y=mx+b and substituting ordered pairs, it's possible to find the intercepts. Doing this yields the equation as y=-x+7.

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