Based on the transmission line approximation, three different equivalent formulations have been proposed for evaluating the interaction between an external electromagnetic field and a transmission line. Moreover, for the line-plane transmission-line, employing the three formulations, C. A. Nucci and F. Rachidi discussed the voltages induced on an overhead line by a nearby lightning strike and, by numerical example, showed that the total induced voltages predicted by these three formulations are identical. This paper, by using an analytic method to discuss the load voltage and current response with the line-plane transmission-line Taylor and Agrawal coupling models, obtained their analytic solutions of the load response for a plane-wave excitation. In the end, it proves that the analytic solutions are equal indeed. In other words, the two coupling formulations are different expressions of the same equations.