def piecewise_linear_continuous(x, x_b, m_1, b_1, m_2):
    """
    Eq. 10. 2-Part Piecewise Linear Continuous Function
    Used to fit D18O_cc-w fractionation versus drip rate. 
    Describes two lines that intersect at x_b.
    
    Parameters
    ----------
    x : numpy array
        independent variable
    x_b : float
        breakpoint for the piecewise linear function.
    m_1 : float
        slope of the line left of x_b
    b_1 : float
        intercept of the line left of x_b
    m_2 : float
        slope of the line right of x_b
    
    Returns
    -------
    y : numpy array
        dependent variable
    """
    
    y=x*0 # initialize y
    
    # Function Left of x_b
    y[x<=x_b] = m_1*x[x<=x_b] + b_1
    
    # Function right of x_b
    b_2 = (m_1 - m_2)*(x_b)
    y[x>x_b] = m_2*x[x>x_b] + b_1 + b_2
    
    return y