Why Did Moses and Elijah Meet Jesus at the Transfiguration?
When one reads the Transfiguration narrative in Matthew 17.1-9, Mark 9.2-9, or Luke 9.28-36, one is presented with an interesting artifact of the times in which the Gospels were written.  Setting aside the transfiguration itself for another time and taking it plainly, one is left to ask:  Why did the disciples see only Moses and Elijah meet with Jesus?  Why not Adam, Noah, Abraham, or even David?

To understand this, one must understand the setting of the narrative.  With Mark widely considered the earliest known Gospel, we'll use his version.  Mark has Jesus lead the disciples from Bethsaida up some 900 metres above sea level to Caesarea Philippi and then, at the start of this passage, onward higher into the foothills of Mount Hermon.  

That setting is significant for a couple of reasons.  First, it is well outside the known area of Jewish settlements.  The northernmost Jewish settlement is further south, south of Lake Semechonitis.  So they are going into a foreign and probably rather uncomfortable land.

Second, and even more importantly, are the thirty-odd pagan temples that have been found on Mount Hermon.  Jesus is effectively leading them among the worship of the sundry pagan religions of the period.

In the midst of these, they see him with Moses and Elijah.  Moses, of course, is known for giving the Torah, or Law.  Elijah is known as the pre-eminent prophet.  But why not someone else?  The reason is: There was no one else to meet with at this time.

In the time of Jesus, the authoritative Jewish Scriptures were not what they are today.  Today, the Jewish Scriptures are called the Tenakh because they are comprised of the Jewish Law (Torah), the Prophets (Hebrew: Nevi'im), and the Writings (Hebrew: Kethuvim).  These eventually formed an anagram as the Tenakh.  

But in Jesus' day, there were no writings.  While the Psalms were referenced, perhaps even sung in the temple, they were not considered part of Scripture such that a Jew could use them for doctrine.  Rather, there were only two parts of Scripture that could be used, the Law and the Prophets.  And Moses and Elijah appear with Jesus to illustrate his being superior to them, being their source and their purpose.