This paper presents an experimental and theoretical investigation of a graphene-integrated electro-absorption modulator (EAM) based on a slot waveguide. Due to the enhanced light-matter interaction of graphene, the device exhibits an impressive modulation efficiency (0.038 dBµm-1V-1) and bandwidth (≈ 16 GHz). Starting from these results, we carried out an extensive design study, focusing on three crucial design parameters and exploring the associated trade-offs in insertion loss, extinction ratio and bandwidth. The simulation results offer valuable insights into the influence of each design parameter, reaffirming that our slot waveguide platform holds great promise for realizing a high-performance EAM balancing optical and electrical performance. It is important to note that the slot waveguide was defined through standard deep ultraviolet (DUV) lithography, allowing seamless integration into high-density systems.