[Matthew] 4:1 led by the Spirit...to be tempted. This testing of Jesus (the Greek verb translated "tempted" can also be rendered "tested"), which was divinely intended, has as its primary background Dt 8:1-5, from which Jesus whether or not you would keep his commands.” Here at the beginning of his ministry Jesus is subjected to a similar test and shows himself to be the true Israelite who lives “on every word that comes from the mouth of the LORD.” And whereas Adam failed the great test and plunged the whole race into sin (Ge 3), Jesus was faithful and thus demonstrated his qualification to become the Savior of all who receive him. It was, moreover, important that Jesus be tested/tempted as Israel and we are, so that he could become our “merciful and faithful high priest” (Heb 2:17) and thus be “able to help those who are being tempted” (Heb 2:15; see Heb 4:15–16). Finally, as the one who remained faithful in temptation he became the model for all believers when they are tempted.
[Matthew] 4:2 forty days and forty nights. The number recalls the experiences of Moses (Ex 24:18; 34:28) and Elijah (1Ki 19:8), as well as the 40 years of Israel’s temptation (testing) in the desert (Dt 8:2–3).
[Matthew] 4:3 If you are the son of God. Meaning "Since you are." The devil is not casting doubt on Jesus' divine sonship, but is tempting him to use his supernatural powers as the Son of God for his own ends.[Matthew] 4:4 Just as God gave the Israelites manna in a supernatural way (see Dt 8:3 and note), so also people today must rely on God for spiritual nourishment. Jesus relied on his Father, not his own miracle power, for provision of food.
Concordia Self-Study Bible, New International Version, p. 1453-1454