Final answer:
The Homestead Act of 1862 provided settlers with cheap or free land in exchange for farming it for 5 years, playing a major role in encouraging westward expansion and the development of the West.
Step-by-step explanation:
The act signed by Abraham Lincoln that gave settlers cheap or free land in the west on the condition that they farm it for 5 years is the Homestead Act of 1862. This was part of the federal government assistance to encourage westward expansion and to populate the Western territories with settlers who supported the concept of free soil, which was land free of slavery. Homesteaders were required to "improve" the land by farming and constructing buildings, turning the vast American frontier into productive farmland. This act was crucial in transferring over 270 million acres of public domain land into the hands of private citizens.