Labelling non-axis lines like axes
I'm trying to draw a line parallel to the axis through a point and label it just like an axis, to illustrate transformations of bases. So I might pick an "origin" (1,2) (according to the original coordinate system), and then draw the lines x=1 and y=2. Then I would like to label (2,2) with a "1", (3,2) with a "2", (0,2) with "-1" and so on, in a different colour from the standard axes, and similarly on the line x=1. I would ideally like to be able to do this without having to manually add lots of points along the new axes. And then if the new origin is moved from (1,2), the axes and numbers would follow along.
Does anyone have any suggestions of whether this could be achieved, and if so, how?