Efforts to parameterize ice shelf basal melting within climate models are limited by an incomplete understanding of the influence of ice base slope on the turbulent ice shelf-ocean boundary current (ISOBC). Here we examine the relationship between ice base slope, boundary current dynamics, and melt rate using 3-D, turbulence-permitting large-eddy simulations (LES) of an idealized ice shelf-ocean boundary current forced solely by melt-induced buoyancy. The range of simulated slopes (3-10%) is appropriate to the grounding zone of small Antarctic ice shelves and to the flanks of relatively wide ice base channels, and the initial conditions are representative of warm-cavity ocean conditions. In line with previous studies, the simulations feature the development of an Ekman boundary layer adjacent to the ice, overlaying a broad pycnocline. The time-averaged flow within the pycnocline is in thermal wind balance, with a mean shear that is only weakly dependent on the ice base slope angle alpha, resulting in a mean gradient Richardson number that decreases approximately linearly with sin(alpha). Combining this inverse relationship with a linear approximation to the density profile, we derive formulations for the friction velocity, thermal forcing, and melt rate in terms of slope angle and total buoyancy input. This theory predicts that melt rate varies like the square root of slope, which is consistent with the LES results and differs from a previously proposed linear trend. The derived scalings provide a potential framework for incorporating slope-dependence into parameterizations of mixing and melting at the base of ice shelves.