def _slope_integral(x, m, b):
    """Indefinite integral of y = mx + b, with an x value substituted in.

    Args:
      x: the x-value
      m: the value of the slope
      b: the y-offset value

    Returns:
      The indefinite integral of y = mx + b, with an x value substituted in.
      (m x^2 / 2 + b x)
    """
    return m * x**2 / 2 + b * x