Final answer:
The band discovered by David Geffen and originally backing Linda Ronstadt is The Eagles, later signed to Geffen's Asylum Records.
Step-by-step explanation:
The band that was discovered by future billionaire David Geffen, and originally served as the backing band for Linda Ronstadt, is The Eagles. The Eagles were formed in the early 1970s and consisted of members Glenn Frey, Don Henley, Bernie Leadon, and Randy Meisner.
David Geffen, the music and film industry executive who would later become a billionaire, played a pivotal role in the band's formation and early success by signing them to his Asylum Records label. With their unique mix of rock, country, and folk sounds, The Eagles went on to become one of the world's best-selling bands of all time.