The standing committees of the House of Representatives and of the Senate in charge of appropriation measures shall sit jointly in open sessions while considering the budget and shall begin such joint meetings within five days after the budget has been submitted to the General Assembly by the State Budget and Control Board. This joint committee may cause the attendance of heads or responsible representatives of the departments, institutions and all other agencies of the State to furnish such information and answer such questions as the joint committee shall require and to these sessions shall be admitted, with the right to be heard, all persons interested in the estimates under consideration. The Board, or its representatives, and the Governor-elect shall have the right to sit at these public hearings and be heard on all matters coming before the joint committee.