Answer:
One must consider the phase difference between each side of the slit:
One can write Δ = W sin θ where Δ is the phase difference between light leaving opposite sides of the slit, W = slit width, and θ is the angle of difraction
As the slit gets wider (W increases) and for a given phase difference the angle of difraction will decrease
The bands on the screen will be closer for a wider slit