I'm starting to study Minkowski diagrams, but I can't figure out how should the axis of a $S'$ system look if it is in rest with respect to the frame $S$. I've seen that in all diagrams the origin seems to stay in place. How is this possible for two frames in rest to respect with each other, one separated from the other 8 light-minutes to agree on the origin? Shouldn't the other frame be "to the right/left"?
Also, if I am an observer on a frame $S''$ moving with a speed $u_x$ with respect to them, how would their axis look to me? Are they axis with the same inclination but located in different places?