Genetic assimilation results from selection on phenotypic plasticity, but quantitative genetics models of linear reaction norms considering intercept and slope as traits do not fully incorporate the process of genetic assimilation. We argue that intercept-slope reaction norm models are insufficient representations of genetic effects on linear reaction norms, and that defining the intercept as a trait is unfortunate. Instead we suggest a model with three traits representing genetic effects that respectively (1) are independent of the environment, (2) alter the sensitivity of the phenotype to the environment, and (3) determine how the organism perceives the environment. The model predicts that, given sufficient additive genetic variation in environmental perception, the environmental value at which reaction norms tend to cross will respond rapidly to selection, and eventually become equal to the mean environment. Hence, in this model, genetic assimilation in a new environment becomes complete without changes in genetic correlations, genetic drift or imposing any fitness costs on maintaining plasticity. The asymptotic evolutionary outcome of this three-trait linear reaction norm generally entails a lower degree of phenotypic plasticity than the two-trait model, and maximum expected fitness does not occur at the mean trait values in the population.