We present a simple model for galaxy attenuation by fitting SKIRT radiative transfer calculations for similar to 10 000 EAGLE galaxies at redshifts z = 2 - 0. Our model adapts the two-component screen model of Charlot & Fall, parametrizing the optical depth and slope of the interstellar medium screen using the average dust surface density, Sigma(dust). We recover relatively tight relations between these parameters for the EAGLE sample, but also provide the scatter in these parameters owing to the morphological variation and orientation of galaxies. We also find that these relations are nearly independent of redshift in the EAGLE model. By pairing our model with an empirical prescription for birth clouds below the resolution scale of the simulation, we reproduce the observed relation between attenuation slope and optical depth for the first time in a cosmological simulation. We demonstrate that this result is remarkably independent of the attenuation properties assumed for the birth cloud screen, merely requiring a boosted attenuation for infant stars. We present this model with a view to interpreting observations, as well as processing semi-analytic models and other hydrodynamic simulations.