Discuss the relationship between the ideology of the American Revolution and the emergence of anti-slavery thinking in the United States and Great Britain.

Both the ideology of the American Revolution and that of abolitionism are grounded in Enlightenment thinking. One of the key notions in Enlightenment political thought was thinking about the nature of human rights. Rather than seeing society as a natural hierarchy with God at the pinnacle, then angels next, then human rulers and aristocrats, then ordinary people, and then animals, plants, and minerals, with those at the top of the hierarchy being naturally better than those at the bottom and thus having more power, the Enlightenment thinkers began with the individual human and saw human associations and hierarchies as something that evolved historically rather than being grounded in a divinely authorized hierarchy.
The Declaration of Independence reflects this form of Enlightenment thought in the first sentence of its second paragraph:

We hold these truths to be self-evident, that all men are created equal, that they are endowed . . . with certain unalienable Rights, that among these are Life, Liberty, and the pursuit of Happiness.

This notion of all people being created equal is the basis of abolitionism. Rather than viewing people as part of a natural hierarchy, something that might justify some being owners and some being slaves, both the founders of the United States and the abolitionists held that all people were created equal. Thus, government is only legitimate insofar as it operates with the consent of the governed. Since slaves do not consent to their slavery but instead have it imposed on them, it is illegitimate according to the Lockean account of government underpinning the Declaration of Independence.