Question

What is the purpose of the letter?

To cause the Church to fight racial injustice
To show society how the church is at fault
To comfort his audience in difficult times
To complain about the unfair treatment in jails

Answer 1

The purpose of King's letter is to cause the Church to fight racial injustice.
As you already know, King was a proponent of equal human rights, for both black, and white people. He wanted the Church to be aware of inequalities in the world and fight racism so as to erase those inequalities.