Phenomenological relations such as Ohm’s or Fourier’s law have a venerable history in physics, but are still scarce in biology. This situation restrains predictive theory. Here, we build on bacterial “growth laws,” which capture physiological feedback between translation and cell growth, to construct a minimal biophysical model for the combined action of ribosome-targeting antibiotics. Our model predicts drug interactions like antagonism or synergy solely from responses to individual drugs. We systematically refine the model by including direct physical interactions of different drugs on the ribosome. In a limiting case, our model provides a mechanistic underpinning for recent predictions of higher-order interactions derived using entropy maximization. It further makes parameter-free predictions for combined drug effects on cells carrying resistance genes and for drugs that mimic poor nutrient environments. We show experimentally that resistance genes can drastically alter drug interactions in notable agreement…