The Book of Matthew {presents Jesus as}
King
Matthew presents Jesus as the fulfilled MESSIAH or KING OF THE JEWS, to the Jews. and he traces Jesus' genealogy from King David, making Him having a royal lineage. Originally written in Greek.
Servant
Reveals Jesus as the SERVANT of God. and originally written in Aramaic = Hebrew.The Book of Luke {presents Jesus as}
Man
Showing Jesus' side of HUMANITY. He traces his genealogy way back to Adam, making Him with all mankind. Originally written in Greek.