The universality and linearity of the Leavitt law are hypotheses commonly adopted in studies of galaxy distances using Cepheid variables as standard candles. In order to test these hypotheses, we obtain slopes of the Leavitt law using linear regressions of fundamental-mode Cepheids observed by the optical gravitational lensing experiment project in the Magellanic Clouds. We find that the slopes in VI bands and in the Wesenheit index behave exponentially, indicating non-linearity. We also find that the slopes obtained using long-period Cepheids can be considered as universal in the VI bands, but not in the Wesenheit index.