Using John Locke, Adam Smith, and Cato’s Letters, describe the ideas leading to the American Revolution and the Declaration of Independence.

When we look at the Declaration of Independence, we see many significant statements that eventually came to represent the values of the United States. Many Americans today would be familiar with "inalienable rights" (rights that cannot be taken away), or the rights to "life, liberty, and the pursuit of happiness." These ideas were not, however, originally developed by Thomas Jefferson, but rather by an English Enlightenment thinker named John Locke. In his Second Treatise on Government, Locke stated that all people had certain inalienable rights and that among those rights were the rights to life, liberty, and property (later altered by Jefferson to be more encompassing). At the time of the Declaration of Independence, it was the belief of many revolutionary leaders that these rights were not being respected by the British government.
Adam Smith, a contemporary of Jefferson and the American Revolution, held the belief that the United States had the right to attempt to achieve their own economic success as a free state. Smith was not in favor of the British economic plan of mercantilism, which involved colonial control. Smith saw mercantilism as being opposed to his free market views. Additionally, in his book The Wealth of Nations, Smith suggested that the United States would not only gain independence but would become one of the strongest nations on earth (as seen in the quote below).

The persons who now govern the resolutions of what they call their continental congress, feel in themselves at this moment a degree of importance which, perhaps, the greatest subjects in Europe scarce feel. From shopkeepers, tradesmen, and attornies, they are become statesmen and legislators, and are employed in contriving a new form of government for an extensive empire, which, they flatter themselves, will become, and which, indeed, seems very likely to become, one of the greatest and most formidable that ever was in the world.

Smith's views of economic independence would certainly be favored by American colonists seeking independence. The prospect of economic freedom would serve as a motivating factor to push for political independence.
Finally we look at the writings and beliefs of Cato. Cato was a pseudonym under which two Englishmen, John Trenchard and Thomas Gordon, wrote. The name Cato references Cato the Younger, an opponent of Julius Caesar who valued liberty and opposed the consolidation of power by Caesar. In Cato's letters (Trenchard and Gordon), there is a great deal of rhetoric supporting freedom and opposing unjust government. Some examples of significant excerpts from Cato's letters linked to the ideals of the American Revolution can be found quoted below.

General liberty . . . is certainly the right of all mankind.
Government executed for the good of all, and with the consent of all, is liberty; and the word government is profaned, and its meaning abused, when it signifies anything else.
Only government founded upon liberty is a public blessing; without liberty, it is a public curse.
All men are born free; liberty is a gift which they receive from God himself.

As you can see in the quotes, the beliefs in Cato's letters focused around liberty and the fact that liberty is a right given by God. It is also made clear that government is expected to protect and respect the liberty of the people, or it ceases to be something necessary to the people. Colonial leaders who had read and agreed with Cato's letters felt that their right to liberty was not being respected by the British government, which pushed them to favor revolution as a response.
Through the examination of the works of John Locke, Adam Smith, and Cato's letters, we can clearly see the impact these political and economic philosophers had on Jefferson and the other leaders of the American Revolution.
https://www.crf-usa.org/bill-of-rights-in-action/bria-23-1-a-adam-smith-and-the-wealth-of-nations.html

https://www.crf-usa.org/foundations-of-our-constitution/natural-rights.html