We study in simple terms the role of feedback in establishing the scaling relations of low-surface-brightness (LSB) and dwarf galaxies with stellar masses in the range 6 × 105≤M*≤ 3 × 1010 M⊙. These galaxies – as measured, for example, from the Sloan Digital Sky Survey (SDSS) and in the Local Group – show tight correlations of internal velocity, metallicity and surface brightness (or radius) with M*. They define a fundamental line which distinguishes them from the brighter galaxies of high surface brightness and metallicity. The idealized model assumes spherical collapse of cold dark matter (CDM) haloes to virial equilibrium and angular momentum conservation. The relations for bright galaxies are reproduced by assuming that M* is a constant fraction of the halo mass M. The upper bound to the low-luminosity LSBs coincides with the virial velocity of haloes in which supernova feedback could significantly suppress star formation, V < 100 km s−1. We argue that the energy fed to the gas obeys ESN∝M* despite the radiative losses, and equate it with the binding energy of the gas to obtain M*/M∝V2. This idealized model provides surprisingly good fits to the scaling relations of low-luminosity LSBs and dwarfs, which indicates that supernova feedback had a primary role in determining the fundamental line. The apparent lower bound for galaxies at V∼ 10 km s−1 may be caused by the cooling barrier at T∼ 104 K. Some fraction of the dark haloes may show no stars as a result of complete gas removal, either by supernova winds from neighbouring galaxies or by radiative feedback after cosmological reionization at zion. Radiative feedback may also explain the distinction between dwarf spheroidals (dE) and irregulars (dI), where the dEs, typically of V≤ 30 km s−1, form stars before zion and are then cleaned out of gas, whereas the dIs, with V > 30 km s−1, retain gas-rich discs with feedback-regulated star formation.