Final answer:
The 1935 New Deal act that guaranteed workers the right to collective bargaining was the Wagner Act, which also formed the NLRB to uphold labor rights and facilitate dispute resolution.
Step-by-step explanation:
The 1935 New Deal act that guaranteed workers the right to collective bargaining is known as the Wagner Act, or formally as the National Labor Relations Act. This pivotal legislation mandated government support for workers seeking to bargain collectively, and it prohibited discrimination against union members. Alongside establishing the National Labor Relations Board (NLRB) to enforce these provisions and settle disputes, the act was instrumental in shaping labor relations in the United States and played a significant role in the growth of union membership during the 1930s. Following its passage, there was a notable increase in industrial unionism, which was further supported by government policies during World War II. Despite challenges, the Wagner Act received constitutional validation from the U.S. Supreme Court and remained a foundational pillar of American labor law.