Jesus as the New Adam
The events surrounding Jesus' baptism remind us of the creation of the world described in Genesis: the Father speaking and the Spirit hovering over the waters. These connections show us that Jesus came to inaugurate a new creation even in the midst of this fallen world. Instead of abandoning the whole project and starting over from scratch, God shows the depth of His mercy and the greatness of His power by redeeming our fallen world from within. God enters into the wreckage in order to undo it.
It shouldn't surprise, then, that Luke's genealogy also links Jesus to Adam, who is called "son of God." The original Adam was not divine, but he had no human father and he was charged to exercise kingly dominion. Thus, son of God is a royal title, not primarily a title of divinity. But Luke's point is to show us that Jesus is a new sort of Adam. A faithful son, a true image bearer of God. Adam failed to guard the garden and defend His bride from the serpent's attack. Adam seized for glory instead of waiting for God to bestow it. Adam refused to trust God's provision and be content with the unbelievable gifts God had provided. And because of their ingratitude and impatience, Adam and Eve chose the word of the serpent over the word of God.
But in His grace, God promised to send a Savior who would undo the effects of the Fall, defeat the Serpent, and redeem the world from the curse of sin and death. As the story of Jesus' temptation shows us, Jesus is the new Adam who was faithful in every way and perfectly obeyed God's word. Jesus is the promised Seed of the woman who came to crush the head of the serpent. Instead of abdicating responsibility, Jesus laid down His life for His Bride. Instead of seizing power and grasping for glory, Jesus laid aside His glory and humbled Himself to die for us.
Jesus as the New David
Another key story playing in the background of Jesus' temptation is that of King David's anointing. The parallels between the beginning of Jesus' ministry and the beginning of David's public life are striking. David was anointed king by Samuel (1 Sam. 16), and the Spirit of God rushed upon David from that day forth. In the very next chapter we read about the Philistine warrior Goliath taunting Saul's army in the wilderness for 40 days. David trusted God's promise and crushed the head of Goliath, who talked like the serpent and even looked like a serpent all dressed up in bronze armor.
All of this points to Jesus as the Greater Son of David and true Son of God who came to crush the head of the real Serpent—the Devil himself. After Jesus' baptism and anointing by the Spirit, He was led into the wilderness for 40 days. Jesus' encounter with and triumph over Satan in the wilderness foreshadows Jesus' victory over Satan in His crucifixion and resurrection.