Graphene is an emerging two-dimensional material with a lot of promising applications as devices, in which it must be combined with other materials, most notably put on top of a substrate. Recent research has shown that certain substrates can change the physical properties of graphene dramatically. Here, we propose a simple model describing a system of single layer graphene on top of a layered insulating substrate based on the tight-binding approximation, where we introduce a hybridization term of the graphene 2pz orbital and topmost substrate layer orbitals. We then calculate the density of states DOS (ν) and the real part of the optical conductivity tensor σ1 ab(ω) of the graphene layer for various values of the substrate band gap. The results show that the graphene-substrate hybridization tends to create states around the Fermi energy, thus enhancing the DC conductivity of the graphene layer. Furthermore, the peak in the σ1 aa(ω) of graphene tends to get renormalized and experience a redshift, most prominently when the substrate band gap matches twice the graphene nearest-neighbor hopping parameter tg. Meanwhile, an insulating substrate with a very high band gap (around 4tg) weakens the effects of the hybridization.