How we cite our quotes: (Paragraph.Sentence)
Quote #1
I say to you today, my friends, so even though we face the difficulties of today and tomorrow, I still have a dream. It is a dream deeply rooted in the American dream. (2.1)
The idea of the American Dream varies from person to person, but it essentially promises that everyone can have a happy, successful, and free life if they're willing to work hard. Linking the dream of racial equality to the overall American dream gives the speech a quality of universality, or relevance to all people. That's pretty generous coming from a minority that was oppressed by the majority.
Quote #2
I have a dream that one day this nation will rise up and live out the true meaning of its creed: "We hold these truths to be self-evident, that all men are created equal." (12.1)
Here's a reference to the Declaration of Independence. The Declaration (which was written by Thomas Jefferson, a slave owner) isn't a legal document. It's more like America's mission statement. Like most mission statements, it got totally and instantly violated—by the continuation of slavery after the Revolution.
Quote #3
I have a dream that one day on the red hills of Georgia, the sons of former slaves and the sons of former slave owners will be able to sit down together at the table of brotherhood. (13.1)
In post-slavery America, a lot of racists justified Jim Crow by suggestion that African Americans and whites could still be equal if they were separated—living in different places, eating at different restaurants, going to different schools, and only marrying within the race. MLK's speech contrasts this with an image of different races being united in brotherhood.