I hope I got your question right. I suppose you have a line originating at (x0/y0) with an angle alpha and a length L:
L=5;alpha=pi/6;
x0=2;y0=1;
figure, hold all
plot([x0 x0+L*cos(alpha)],[y0 y0+L*sin(alpha)])
axis equal
Secondly, you have a distance s smaller than L and you want all steps of size s on that original line, right?
s=.5;
xs=x0+(0:s:L)*cos(alpha);
ys=y0+(0:s:L)*sin(alpha);
plot(xs,ys,'o')
If you don't want (x0/y0) to be part of (xs/ys), just increment starting from s instead of starting from 0.
