In short
The section of Matthew’s genealogy that focuses on David as the king
and on his royal descendants shows that Jesus also is a King in David’s line.
Matthew 1:6–11 traces the genealogy from David’s kingship to the time of the Babylonian captivity. The fact that David is here expressly described as a king
emphasizes the royal nature of the genealogy and by extension Jesus’ claim to the throne of David, which by that time had been vacant for so long.1
6 and Jesse the father of David the king.And David was the father of Solomon by the wife of Uriah,