Final answer:
No article in the United States Constitution allows for amendments to originate directly by petition of the voters. The amendment process is outlined in Article V, which requires a two-thirds vote in Congress or a convention called by two-thirds of the State legislatures.
Step-by-step explanation:
The question asks for which article in the Constitution amendments may originate by petition of voters. According to Article V of the United States Constitution, the process for amending the Constitution is outlined. Amendments can be proposed either by Congress with a two-thirds majority vote in both the House of Representatives and the Senate or by a constitutional convention called for by two-thirds of the State legislatures. However, there is no provision in the Constitution for amendments to originate directly by petition of the voters. Therefore, none of the options listed, that is, Article I, Article II, Article III, or Article IV, allow for amendments to originate through a voter petition.