Final answer:
The Missouri Compromise of 1820 allowed Missouri to join as a slave state and Maine as a free state, preserving the Senate balance, and established the 36°30' line to limit the spread of slavery in the Louisiana Purchase.
Step-by-step explanation:
The compromise in the 1800s that allowed Missouri to enter as a slave state and Maine as a free state, maintaining the balance of power in the Senate between slave states and free states, is known as the Missouri Compromise. Enacted in 1820, the Missouri Compromise was spearheaded by Henry Clay and aimed to address the sectional conflicts arising from Missouri's request to enter the Union as a slave state. To prevent future conflicts, the compromise established the 36°30' line across the Louisiana Purchase territory as the division between where slavery was permitted and where it was banned, with slavery being allowed to the south of this line and prohibited to the north, ensuring a balance between free and slave states in the Senate