Recent studies of genetically modified enzymes have indicated that changes in activation free energies, Delta Delta g(double dagger), and changes in reaction free energies, Delta Delta G(0), are correlated by the relationship Delta Delta g(double dagger) = beta Delta Delta G(0). The present work explores the basis for such linear free energy relationships (LFERs) in enzymatic reactions, focusing on the effects of mutations in tyrosyl-tRNA-synthetase (TTS). It is demonstrated that the optimal way to analyze LFERs is by describing the reaction in terms of pure valence bond (VB) resonance structures rather than in terms of partially formed bonds. The use of the pure VB representation allows one to evaluate the relevant LFER using Marcus-type concepts and to compare the predicted beta to the observed one. Using a two-resonance-structure VB model for TTS produces beta similar or equal to 0.5, which disagrees with the observed values of beta similar or equal to 0.83 and beta >> 1 for two classes of mutations. Noting, however, that the phosphoryl transfer process in TTS has been described before as going through a high-energy intermediate, we describe this reaction in terms of three VB resonance structures. This accounts for the observed values of beta and supports the validity of LFER in TTS. It is pointed out that LFERs are valid in proteins even when the changes in Delta g(double dagger) involve very anharmonic interactions like hydrogen bonds, since such relationships reflect the correlation between Delta Delta g(double dagger) and Delta Delta G(0) rather than the correlation between Delta Delta g(double dagger) and the effect of specific residues. However, obtaining LFER in proteins requires that the active site environment responds linearly to the change of charges during the reaction, and such a linear response is far from obvious. Fortunately, the simulation study presented in this work as well as previous simulations has demonstrated that active sites of proteins obey the linear response approximation. Such a behavior of highly anharmonic systems is due to the availability of many compensating polar interactions. This finding provides a theoretical basis for the experimental observation of LFER in TTS.