Missouri was not the first state carved out of the Louisiana Purchase territory - Louisiana, which became a state in 1812, entered the Union first. But admittance of Louisiana as a slave state merely re-established a balance between free and slave states that had existed since the country's beginning.
The admission of Missouri proved controversial, however. Slavery already existed in the Missouri territory, but when the Missouri statehood bill came before the House of Representatives in 1819, a northern representative proposed an amendment that would have banned the expansion of slavery in Missouri and eventually eliminated it. The House passed the amendment; the Senate defeated it. For southerners, passage of the amendment would have swung control of the Senate, where an equal number of free and slave states were represented, into northern hands, just as had happened in the House because of population growth in the North.
With a request for admission of Maine as a state, the way was opened for a compromise solution. In March 1820, Maine and Missouri were admitted as states, thus maintaining the Senate balance. At the same time, the issue of how slavery would be determined with regard to other states carved from the Louisiana Purchase territory was determined. Henceforth, with the exception of Missouri, slavery was prohibited in states created from that territory that were north of the 36 30' parallel line. This prohibition remained in effect until passage of the Kansas-Nebraska Act in 1854 opened the door to determination by popular sovereignty and the Supreme Court declared as part of the Dred Scott decision of 1857 that the Missouri Compromise was unconstitutional.
Further Reading:
Forbes, Robert Pierce. The Missouri Compromise and Its Aftermath: Slavery and the Meaning of America. Chapel Hill: University of North Carolina Press, 2007.