how does matthew's gospel show that jesus is the king?
Matthew's Gospel depicts Jesus as the King who would one day rule on David's throne as a human king. It traces His genealogy through Abraham, Isaac, and Jacob, and down the royal family of David, presenting Him in His humanity as the King from David's royal family.
Les explains that Matthew, Mark, and Luke are called the Synoptic Gospels because they deal with Christ in His humanity. Matthew in particular depicts Him as the King who would one day rule on David's throne as a human king, coming through the genealogy of Abraham, Isaac, and Jacob and down David's royal family. Mark presents Him as the servant, and Luke as the Son of Man. John, by contrast, depicts Him as the Son of God in His deity. Les also notes that Matthew, Mark, and Luke record His wilderness temptations, while John omits them because those temptations affected His human side, not His deity.