Luke 3 records the ministry of John the Baptist, Jesus’ baptism, and the voice from heaven. With respect to Jesus’ early years, Matthew, Mark, and Luke all follow the same basic order of events: birth, baptism, voice from heaven, and then wilderness temptation.
But Luke uniquely offers us Jesus’ genealogy between the baptism and the temptation. This is a curious placement for a genealogy, and at first pass it might seem to interrupt the flow of Luke’s narrative. We might expect Luke to place the genealogy at the beginning of his Gospel (such as we find in Matthew), or perhaps at the end of Luke chapter 1, right before Jesus’ birth. Yet Luke strategically places it here, just prior to the wilderness temptation.
The key to understanding the placement of the genealogy is found within the genealogy itself. Unlike Luke, Matthew’s gospel is written to the Jewish community. As such, Matthew’s genealogy (presumably following Joseph’s line) links Jesus to King David, the greatest of the Jewish Kings, and then to Abraham, the father of the Jewish people. And there Matthew’s genealogy stops. But Luke’s gospel is written to a non-Jewish audience, and his genealogy does not focus on Jesus’ relation to Abraham. Instead, Luke (presumably following Mary’s line) traces Jesus all the way back to Adam, and then ultimately to God.
Matthew’s genealogy presents Jesus as the second David, a son of Abraham. Luke’s genealogy presents Jesus as the second Adam, a son of God.
And thus Luke offers us the genealogy — linking Jesus to Adam, and ultimately to God — as a means of introducing Jesus’ wilderness temptation. It is Jesus — the decedent of Adam and the Son of God — who will overthrow the Devil. With the placement and nature of his genealogy, Luke intends us to see Jesus’ wilderness temptation as a recapitulation of Adam’s garden temptation.
Where the first Adam failed, the Second Adam would succeed.