On what covenant is Jesus’s entire earthly ministry based?
Jesus’s entire earthly ministry is based on the covenant God swore to Abraham—the Abrahamic covenant. Luke 1 connects the promised mercy to the oath made to the fathers, going back to Abraham, and Matthew 1 likewise traces the line to Abraham. Everything Jesus does in His earthly ministry rests on that covenant.
Les explains that the covenant in view is the oath God swore to Abraham, as Luke 1:72-73 shows. He points out that Zacharias understood the prophetic plan: the king would come, Israel would have her kingdom, and the promised mercy was for Israel in the house of David, not the Gentiles. Matthew 1 and Luke 1 both go back to Abraham. Les emphasizes that everything Jesus does in His earthly ministry is based on that covenant, and he wishes people could see it.
The oath which he sware to our father Abraham,