She also saluted King for “navigating the politics of an era that didn’t make space for a female genius. Slowly but surely Carole King worked to create one, and it will be hers forever.”

After thanking Swift “for carrying the torch forward” and calling her “like my professional granddaughter,” King paid tribute to Goffin and other collaborators and supporters, including Tapestry album producer Lou Adler and James Taylor, as well as musicians, managers and others.

“I keep hearing it, so I’m gonna have to try to own it, that today’s female singers and songwriters stand on my shoulder,” said King. “Let it not be forgotten they also stand on the shoulders of the first woman to be inducted into the Rock and Roll Hall of Fame. May she rest in power – Miss Aretha Franklin,” she said, to a huge ovation from the arena crowd. King then introduced Jennifer Hudson, start of the Franklin biopic Respect, who delivered a powerhouse version of the King-written Franklin hit “(You Make Me Feel Like) A Natural Woman” (which King also later recorded for her own Tapestry).

“Ms. Franklin was the one who inspired me; she said ‘Jennifer, always use your voice,’” Hudson, who co-wrote “Here I Am” with King for Respect, told the crowd. “And it was Miss King who told me to use my words. ‘Your voice means nothing if you can’t have your words.’ That means so much.”

King, joined by longtime backing musicians Danny Kortchmar, Leland Sklar and Russell Kunkel, and their band the Immediate Family, closed the segment with her “You’ve Got a Friend,” which had the audience singing along.

The Rock Hall inductions were filmed by HBO and will be aired starting Nov. 20.

Watch a clip of Swift’s live rendition of King’s “Will You Love Me Tomorrow” below.