The Missouri Compromise helped to do two things:
1) Maintain a balance of political power between slave and free states in Congress.
2) Find a temporary "solution" for how to deal with slavery in territories that were becoming US states.
In the Missouri Comprise it was agreed upon that Missouri would enter the US as a slave state, Maine would enter as a free state, and the 36'30 parallel would be used as a border to determine whether or not new states added to the US would have slavery.
The Compromise of 1850 was also reached in order to settle differences between northern and southern politicians about slavery and new territories becoming US states. In this compromise, there were 4 conditions:
1) California would enter the US as a free state.
2) New Mexico and Utah would get to pick whether or not they had slavery (also known as popular sovereignty)
3) Slave trade is banned in Washington DC.
4) A strict new Fugitive Slave Law is passed. This law states that any slaves that escape to the North must be returned to their owners in the South.
The Compromise of 1850 effectively gets rid of the Missouri Compromise. Neither of these laws stayed in place for very long, as the Civil War results in slavery being outlawed across the entire US.
