Final answer:
President Polk's administration favored extending the Missouri Compromise line, also known as the 36°30' line, to decide the future of slavery in new territories.
Step-by-step explanation:
President Polk's plan for determining the status of slavery in new territories involved extending the Missouri Compromise line. This line, also known as the 36°30' line, was originally part of the Missouri Compromise of 1820, which regulated slavery in the western territories.
The compromise line essentially allowed slavery below the latitude 36°30' and prohibited it above. James Buchanan, Polk's Secretary of State, supported the idea of extending this line all the way to the Pacific Ocean. However, the proposal was voted down by the House, despite receiving multiple affirmative votes in the Senate, indicating the contentious nature of the slavery issue during this period.