What are the two methods for proposing an amendment to the Constitution?

To propose an amendment to the Constitution, there are two established methods as outlined in Article V of the Constitution. The first method requires a 2/3 majority vote in both the House of Representatives and the Senate, ensuring that a significant consensus is achieved among elected representatives at the federal level. The second method allows for a Constitutional Convention to be called by two-thirds of the state legislatures, enabling states to initiate a formal process for amending the Constitution outside of Congressional action.

This bicameral legislative process and the provision for a state-driven convention represent a balance between federal and state power in making significant changes to the nation's foundational legal document. The other options presented do not accurately reflect the constitutional procedures, as they either suggest incorrect voting majorities, include roles that are not constitutionally authorized, or omit necessary legislative procedures.