Final answer:
The purpose of the colonies' emphasis on peaceful means was to seek redress for their grievances and secure their rights from the king of England without rebellion or independence.
Step-by-step explanation:
The purpose of the colonies' emphasis on their efforts to use peaceful means to gain just treatment from the king of England was to seek redress for their grievances while avoiding outright rebellion or independence. The colonists believed they were entitled to their 'natural rights' and that the British government had violated these rights through oppressive policies and actions.
They had repeatedly petitioned the king for redress and sought a peaceful resolution to their grievances. However, their peaceful efforts were met with repeated injury and unsatisfactory responses from the king and Parliament. Through peaceful means, the colonies hoped to secure their rights and establish a fair and just relationship with the king of England, without severing ties with the British Empire.