Final answer:
The Missouri Compromise maintained the balance between slave and free states by admitting Maine as a free state and Missouri as a slave state. It also established the 36°30' line, which prohibited slavery north of that line.
Step-by-step explanation:
The significance of the Missouri Compromise was that it maintained the balance between slave and free states in the United States. It allowed for the admission of Maine as a free state and Missouri as a slave state, thus keeping the number of slave and free states equal. Additionally, it introduced the 36°30' line, which prohibited slavery north of that line in the rest of the land acquired in the Louisiana Purchase.