Final answer:
The right referred to by the writers of the Declaration of Independence is the unalienable rights to life, liberty, and the pursuit of happiness. Governments are established to protect these rights, and should they fail, the people have the right to alter or abolish them.
Step-by-step explanation:
The writers of the Declaration of Independence, influenced by Enlightenment thinkers like John Locke, claimed that everyone is born with certain unalienable rights. These rights include life, liberty, and the pursuit of happiness. The Declaration emphasized that it is the duty of the government to protect these rights, but if it fails to do so, it is the right and duty of the people to alter or abolish that government and institute a new one that will secure their future safety and happiness.
As Thomas Jefferson penned in the iconic document, "We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of happiness."