The last words of chapter three are the conclusion of the genealogy of Jesus: “Adam, the Son of God.”
Luke recognizes that Jesus is for Jew and Gentile alike. Matthew traces the Savior’s line back to Abraham, the father of the nation of Israel. By hearkening back to Adam, Luke tells the reader that this story is not just for Jews, it’s for everyone.
It’s also a wonderful segue to the temptation of Jesus in the desert. Consider the contrast between Adam and Jesus, referred to by Paul (a traveling companion of Luke) as “the Second Adam” in his letter to the Romans. Adam is in the garden; Jesus, in the desert. When Adam is hungry, he eats; Jesus fasts. When Adam is tempted, he sins. Therefore his male descendents are required to be subsistence farmers, more or less. When Jesus is tempted, he obeys God (here and unto the cross), and so all of his descendents bear the fruit of the Spirit. We are the new Garden, and God walks among us in the cool of the day; covered by his mercy, we are unashamed.