We apply renormalization group theory directly to the first-order phase transition of the large-N model driven linearly by an external magnetic field H--H t, where H is the sweeping rate. Novel dynamic, scaling forms for the magnetization., the structure factor, and the area of hysteresis loop are M (H,t,T)=f(H1/2t, H(d-2)/4T), C(k,H,t,T)=H-d/4f1(H-1/4k, H1/2t, H(d-2)/4T), and A=H1/2g(H(d-2)/4T), respectively, where T is the temperature of the system, d the spatial dimensionality, k the wave number, and f, f1, and g scaling functions. These results show that the rate of the external driving field can serve as a scaling parameter to study hysteresis.