Equilibrium question

I need some help with part c. I understand that if the temperature of this reaction is decreased, the equilibrium shifts in favour of the exothermic reaction, and the rate of reaction between H2 and Cl2 increases.
But I don't know how to show this using the Boltzmann curve; surely if the temperature decreases, there is a decrease in the average energy of the molecules present and so a smaller proportion of molecules are able to react, leading to a decrease in the rate of reaction.These two ideas don't match up, can someone explain this?

I don't think you need to talk about equilibrium in part c), it only asks about the rate of reaction. Also, these two things don't actually effect each other. if the rate decreases, it doesn't necessarily effect the position of equilibrium (although the change of temp. would in this case), it just changes how quickly equilibrium is reached. So I think in this part of the question you just need to draw your curve and explain why the rate of reaction is reduced?