Galaxies fall into two clearly distinct types: 'blue-sequence' galaxies which are rapidly forming young stars, and 'red-sequence' galaxies in which star formation has almost completely ceased. Most galaxies more massive than ... follow the red sequence, while less massive central galaxies lie on the blue sequence. We show that these sequences are created by a competition between star formation-driven outflows and gas accretion on to the supermassive black hole at the galaxy's centre. We develop a simple analytic model for this interaction. In galaxies less massive than ..., young stars and supernovae drive a high-entropy outflow which is more buoyant than any tenuous corona. The outflow balances the rate of gas inflow, preventing high gas densities building up in the central regions. More massive galaxies, however, are surrounded by an increasingly hot corona. Above a halo mass of ..., the outflow ceases to be buoyant and star formation is unable to prevent the build-up of gas in the central regions. This triggers a strongly non-linear response from the black hole. Its accretion rate rises rapidly, heating the galaxy's corona, disrupting the incoming supply of cool gas and starving the galaxy of the fuel for star formation. The host galaxy makes a transition to the red sequence, and further growth predominantly occurs through galaxy mergers. We show that the analytic model provides a good description of galaxy evolution in the EAGLE hydrodynamic simulations. So long as star formation-driven outflows are present, the transition mass scale is almost independent of subgrid parameter choice. (ProQuest: ... denotes formulae/symbols omitted.)