Notice the extended metaphor in lines 17-31. What is the metaphor that is found in the lines 17-31 and what is Dr. King trying to say with this metaphor?

An extended metaphor with which Dr King compares the failure of the government to cater for her black African-American citizens to a bounced or failed check.

Explanation:

A metaphor is a figure of speech used to describe a object or scenario by comparing it with another object or thing. (for example 'light of hope to millions of Negro slaves'  as used in line 2 of the Speech)

In lines 17-31 of the 'I Have A Dream Speech' by Dr Martin Luther King, Dr. King uses an extended metaphor to describe the failure of the US Government to cater for the rights of its African-American citizens by comparing the Government's action to a bounced check  which is symbolic of a failed promise or promises.

The promise to all Americans regardless of race or color as enshrined in the American constitution was a guaranteed access to civil rights and liberties.

That promise was however not granted to the African-American  community during Dr King's lifetime prior to making the famous speech

the answer is slaves

douglas was a slave who turned into a statesman and he refused to celebrate the 4th of july until all slaves were emancipated or set free.