Justinian is considered to be the last Roman Emperor to speak Latin as a first language. What does this fact imply about the changes in the Roman Empire at that time?

It implies the focus of the empire as a whole was moving away from the Western half. The West was poor and stretched to thin to face the germanic hordes. Rome had been sacked multiple times and just never returned to what it once was. This time of weakness for the Western half of the empire provided the opportunity for the eastern half to become prominent and the cultural and political center for the Roman people. The fact that Justinian was the last emperor to speak latin showed how a complete shift had taken place in Roman society. Suddenly Greek became the language of choice and Byzantium became the most important part of the empire. In short it illustrates the fall of the west and rise of the east.