An equation solver to solve: given two points on a line and x, solve the
    y coordinate on the same line.

    Suppose p1 = (x1, y1), p2 = (x2, y2), p3 = (x3, y3) on the same line.
    given x1, y1, x2, y2, x3, find y3::

        y3 = y1 - (y1 - y2) * (x1 - x3) / (x1 - x3)

def locate(x1, y1, x2, y2, x3):
    """An equation solver to solve: given two points on a line and x, solve the
    y coordinate on the same line.

    Suppose p1 = (x1, y1), p2 = (x2, y2), p3 = (x3, y3) on the same line.
    given x1, y1, x2, y2, x3, find y3::

        y3 = y1 - (y1 - y2) * (x1 - x3) / (x1 - x3)
    """
    return y1 - 1.0 * (y1 - y2) * (x1 - x3) / (x1 - x2)