Final answer:
The Missouri Compromise established the latitude line at 36° 30' to separate free and slave territories in the Louisiana Purchase lands.
Step-by-step explanation:
The latitude line of the Missouri Compromise was set at 36° 30'. This compromise, reached in 1820, allowed Missouri to enter the Union as a slave state and Maine as a free state, maintaining the balance between free and slave states. The compromise also stipulated that in the rest of the Louisiana Purchase lands, slavery would be prohibited north of this latitude line, while it could expand to the south of it. Ultimately, this was a temporary measure to prevent conflicts over the spread of slavery into new territories and states but would be contested in the following decades leading to the Civil War.