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How to Write in Point-Slope Form an Equation of the Line Through Two Pairs of Points

With four different points, you can not only find the equation of a line in its point-slope form, you can check it, too. Points within the two-dimensional Cartesian coordinate system have two values: an x-coordinate and a y-coordinate. These coordinates indicate how horizontally and vertically far away the point is from the origin, which is the system's center. When you have a pair of points, you can find the linear equation of the line that connects them by the point-slope form, which is (y - y0) = m * (x - x0) where x0 and y0 correspond to coordinates of a single point and m represents the line's slope.

Instructions

    • 1

      Select one of the pairs of points. For example, the pairs of points might be the pair (1, 2) and (2, 4), and the pair (3, 6) and (4, 8). With this example, select (1, 2) and (2, 4).

    • 2

      Label the first point as (x1, y1) and the second point as (x2, y2). In this example, x1 equals 1, y1 equals 2, x2 equals 2, and y2 equals 4.

    • 3

      Subtract x1 from x2 and y1 from y2, and then divide the y-difference by the x-difference to find the line's slope. In this example, 2 - 1 equals 1, 4 - 2 equals 2, and 2 divided by 1 equals 2.

    • 4

      Substitute the slope calculated from the last step for m in the equation (y - y0) = m * (x - x0). With this example, the equation becomes (y - y0) = 2 * (x - x0).

    • 5

      Substitute one point's x-coordinate for x0 and the same point's y-coordinate for y0 to complete the point-slope form. Concluding this example, selecting the point (4, 8), the equation becomes (y - 8) = 2 * (x - 4).

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