On April 22, 1978, the Blues Brothers made their first performance on Saturday Night Live. Although the act can trace its earliest incarnation to a 1976 sketch where John Belushi sang "I'm a King Bee," the full Blues Brothers concept only took shape in 1978. This was the first time we saw Jake and Elwood wearing suits, Wayfarers, and performing with their full band.
On that night, Paul Shaffer introduced the boys, claiming that they had been discovered in 1969 by the fictional "Marshall Checker." He spun the yarn further, suggesting that the boys were washed-up hacks. He finished, "Today they are no longer an authentic blues act, but have managed to become a viable commercial product. So now, let's join 'Joliet' Jake and his silent brother Elwood—the Blues Brothers." Shaffer had helped Belushi and Dan Aykroyd recruit most of the band, and his wink-and-nod intro led into a rip-roaring performance of "Hey Bartender" and "I Don't Know."
Although that night's SNL performance is something you have to pay for, there is 1978-era material online for free. The band performed extensively throughout the year, recording Briefcase Full of Blues and rounding out the year with a December 31 show closing the Winterland in San Francisco. That entire performance is online: