QUASARS and active galactic nuclei often have radio jets emanating from them, parts of which sometimes appear to move faster than light(1), These jets are thought to arise from processes associated,vith a supermassive black hole, but it is difficult to study them in detail both because they lie at extreme distances and because observable changes in them occur only slowly. The Galactic ’microquasar’ GRS1915+105 has attracted much attention because it also has superluminal jets(2); it might be a low-power analogue of the ’central engine’ of quasars, but so far the only evidence that it contains a black hole is its X-ray luminosity, which is greater than that allowed for a neutron star, Here we report observations of near-infrared jets from GRS1915+105; these jets emerge at the same position angle as the radio jets, but the luminosity associated with them is far greater, Using these data, we find a correlation between the length of a jet, its brightness temperature and the central source luminosity which applies across the entire range of black-hole-driven jets, thereby connecting microquasars, active galactic nuclei and quasars, Because the evolution of GRS1915+105 can be studied on relatively short timescales, we effectively have the ability to investigate evolutionary processes in quasars.