How does Martin Luther King Jr. support his claim that racial segregation is discriminatory and unjust?

Although slavery in the United States ended in the late 19th century, institutionalized racism continued to oppress African Americans even decades later. By the mid-20th century, blacks were still forced to use separate public utilities and schools from the superior ones reserved for whites; they suffered routine discrimination in employment and housing, as well as abuse and lynching from some whites, and they were unable to fully exercise their right to vote.