Final answer:
The Kansas-Nebraska Act was the federal legislation that embedded Douglas's opinions on addressing slavery in the territories. It proposed to create two territories and apply the principle of popular sovereignty, allowing the people of the territories to decide whether to adopt slavery.
Step-by-step explanation:
The federal legislation that formally embedded Douglas's opinions on addressing slavery in the territories was the Kansas-Nebraska Act.
The Kansas-Nebraska Act was proposed by Stephen Douglas in 1854 and it proposed to create two territories, Kansas and Nebraska, and to apply the principle of popular sovereignty. This meant that the people of these territories would decide for themselves whether to adopt slavery.
By repealing the Missouri Compromise line, the Kansas-Nebraska Act allowed for the possibility of slavery in these territories.