def linear_interpolation(x, nodes):
    for i in range(len(nodes) - 1):
        x0, y0 = nodes[i]
        x1, y1 = nodes[i+1]
        if x0 <= x <= x1:
            t = (x - x0) / (x1 - x0)
            return y0 + t * (y1 - y0)
    return 0.0