Controlling Subplot sizes while using axis image

Hi, I'm trying to produce a nice figure that is being mean to me...

Basically, I want a subplot with an image on the left and a plot on the right that is of the same height as the image and a controllable width. I'm using axis image since I want the pixels of my image not to be stretched. Here is my code to subplot both at the moment:

subplot(1,2,1)
imagesc(Image); 
caxis([5 9]); axis image; colormap(gray);

subplot(1,2,2)
h2 = plot(x,y);
axis([-inf, inf, 0.6, 2.1])

The problem is when I do that, the plot is a lot bigger than the image while I'd like the opposite.

Thanks for the help.