We study optical effects in a hybrid system composed of a semiconductor quantum dot and a spherical metal nanoparticle that interacts with a weak probe electromagnetic field. We use modified nonlinear density matrix equations for the description of the optical properties of the system and obtain a closed-form expression for the linear susceptibilities of the quantum dot, the metal nanoparticle, and the total system. We then investigate the dependence of the susceptibility on the interparticle distance as well as on the material parameters of the hybrid system. We find that the susceptibility of the quantum dot exhibits optical transparency for specific frequencies. In addition, we show that there is a range of frequencies of the applied field for which the susceptibility of the semiconductor quantum dot leads to gain. This suggests that in such a hybrid system quantum coherence can reverse the course of energy transfer, allowing flow of energy from the metallic nanoparticle to the quantum dot. We also explore the susceptibility of the metal nanoparticle and show that it is strongly influenced by the presence of the quantum dot.