The arrangement of ions near a metallic electrode is crucial to energy storage in electrical double-layer capacitors. Classic Poisson-Boltzmann theory predicts that the charge stored in the double layer is a continuous function of applied voltage. However, recent experiments and simulations strongly suggest the presence of a voltage-induced first-order phase transition in the electrical double layer, leading to a hysteretic response: the capacitance-voltage relation is dependent on whether the voltage is increasing or decreasing. By developing a simple analytical model, we show that ion-image interaction could explain this phase transition. Moreover, our model shows that the presence of phase transition depends on the bulk energy of the ionic liquid. Our results justify mixing ionic liquids with solvents as a way to achieve large capacitance and avoid hysteresis.