The interaction between plasmonic resonances, sharp modes, and light in nanoscale plasmonic systems often leads to Fano interference effects. This occurs because the plasmonic excitations are usually spectrally broad and the characteristic narrow asymmetric Fano line-shape results upon interaction with spectrally sharper modes. By considering the plasmonic resonance in the Fano model, as opposed to previous flat continuum approaches, here we show that a simple and exact expression for the line-shape can be found. This allows the role of the width and energy of the plasmonic resonance to be properly understood. As examples, we show how Fano resonances measured on an array of gold nanoantennas covered with PMMA, as well as the hybridization of dark with bright plasmons in nanocavities, are well reproduced with a simple exact formula and without any fitting parameters.