Using the conventional rate equations describing an injection-locked system, a novel modulation response function is derived, which implicitly incorporates nonlinear gain through the free-running relaxation oscillation frequency and damping rate of the slave laser. In this paper, it is shown that the model presented can be used to extract the characteristic parameters of the coupled system from experimental data. The number of fitting parameters in the model is reduced by determining the fundamental slave parameters through the conventional free-running response function; these parameters are considered to be constant during the curve-fitting of the injection-locked system. Furthermore, in order to reduce the number of possible solutions generated during the least-squares-fitting process, the remaining fitting parameters are tightly constrained based on the physical limits of the coupled system. By reducing the number of unknown fitting parameters and constraining the remaining terms, a stronger confidence in the extracted parameters is achieved. Using a series of response curves measured from an injection-locked quantum dash laser, characteristic parameters of the system are extracted and validity of the model is examined. The verified model is used to analyze the impact of the linewidth enhancement factor on the characteristics of the response function in the microwave domain.