1.18 This is how the birth of Jesus the Messiah came about [a]: His mother Mary was pledged to be married to Joseph, but before they came together, she was found to be pregnant through the Holy Spirit. 19 Because Joseph her husband was a righteous man and did not want to expose her to public disgrace, he had in mind to divorce her quietly.
20 But after he had considered this, an angel of the Lord appeared to him in a dream and said, “Joseph son of David, do not be afraid to take Mary home as your wife, because what is conceived in her is from the Holy Spirit. 21 She will give birth to a son, and you are to give him the name Jesus, [b] because he will save his people from their sins.”
22 All this took place to fulfill what the Lord had said through the prophet: 23 “The virgin will conceive and give birth to a son, and they will call him Immanuel” [c] (which means “God with us”).
24 When Joseph woke up, he did what the angel of the Lord had commanded him and took Mary home as his wife. 25 But he had no union with her until she gave birth to a son. And he gave him the name Jesus (TNIV).
Put yourself in Joseph’s shoes: your fiancé’s pregos but you know it’s not your baby… Joseph nevertheless decides against putting Mary through the shame of a public trial; instead, he plans to divorce her quietly.
But then the angel comes and assures him that Mary’s pregnancy is not the result of her unfaithfulness but is the work of the Holy Spirit. Mary will give birth to a son who is to be named Jesus. This was a common Greek name in the first century, but the Hebrew translation behind it, Yeshua, means “Yahweh is salvation” or “Yahweh saves.” Matthew makes sure this is not lost on his readers: “because he will save his people from their sins.”
Matthew further adds that this is all happening in order to fulfill Isaiah’s prophesy that a son would be born and called Immanuel (i.e., “God with us”; Isa. 7.14). This same child in Isaiah is also to be “born for us” and referred to as “the Mighty God, the Everlasting Father, and Prince of Peace” (9.6; France, Gospel of Matthew, 57).
In Jesus, God has come to earth to dwell among his people and to save them from their sins. Jesus therefore embodies both names: He is our savior and He is God with us (see also Matthew 28.20).
Joseph believes the angels words and accepts Mary as his wife. And by naming Jesus—an event reserved for the father—Joseph formally adopts the baby as his own. This is significant because it legally solidifies Jesus’ place in the Davidic line (see v. 20 where Joseph is explicitly referred to as the “son of David”; France, Matthew, 47-48 n. 25; 53). Jesus is therefore the true and legitimate Son of David—He is the King that Israel has been waiting for.
Nicholas Deyo Scherer 
Thanks for explaining the lineage. I had never understood why Jesus was considered a descendent of David, when Joseph wasn’t his biological father.
It’s significant that Joseph is called a righteous man for not following the letter of the law regarding Mary’s apparent infidelity. Righteousness is a key concept in Matthew. In Chapter 12 he quotes Isaiah 42:1-3 “A bruised reed he will not break, and a dimly burning wick he will not quench; he will faithfully bring forth justice.” Like Mary, these are damaged goods that would be thrown away. God’s righteousness and justice encompass compassion, and he does not give as the world gives.