In this paper, we propose a mathematical model to describe the relation between the formant frequencies of speakers and show that with the proposed affine model, speaker differences separate out as translation factors when a "mel-like" warping is performed. Using speech data we estimate the parameters of this warping function and show that it is close to the usual mel-formula. This model is motivated by Rohit et al.'s shift-based non-uniform speaker-normalization method, which provides improvement over the conventional maximum-likelihood based speaker normalization methods. We therefore provide a unified framework that relates the relationship between formants of speakers and method of removing speakers difference (which involves mel-warping) in a neat mathematical framework which is substantiated by our recognition experiments.