Final answer:
The slogan used by the colonists in protest was "No Taxation Without Representation", signifying their stance that only their own legislatures had the right to tax them, not a Parliament where they had no elected representatives.
Step-by-step explanation:
The slogan that the colonists began using in protest of the acts imposed by the English Parliament was "No Taxation Without Representation". This phrase captured the fundamental grievance of the colonists, who felt that since they could not elect representatives to the British Parliament, any taxes it imposed on them were unjust. The concept was based on the principle that only the colonial legislatures, which represented the colonists directly, had the authority to levy internal taxes. The British Parliament, however, did not recognize this distinction, believing in virtual representation and the idea that all British subjects had to obey laws passed by Parliament. This conflict in understanding and the lack of direct representation for the colonists in the British legislative process was a core driver for the revolutionary sentiment that led to the American Revolution.