Final answer:
The Missouri Compromise and Missouri Crisis are the two names given to the 1820 event dealing with slavery's expansion in the Louisiana Territory.
Step-by-step explanation:
The two names given to the 1820 event that dealt with the spread of slavery into the Louisiana Territory are the Missouri Compromise and the Missouri Crisis. This was a significant turning point in the sectional crisis between the North and the South regarding slavery in new territories. The event was marked by the debate over Missouri's admission to the Union, with an initial proposal to gradually abolish slavery in the new state leading to extensive national controversy. Eventually, Congress reached a compromise which allowed Maine to enter as a free state and Missouri as a slave state, with the 36° 30′ parallel establishing a geographic boundary for the future expansion of slavery within the Louisiana Purchase.