If You have a Cartesian co-ord system of x, y, z with origin set at 0,0,0 then you need to add or subtract from the x, y, z of the function by the amount you are moving the origin.
Ie if y=3x at origin x0,y0 then at a new origin x4,y3 the function will be y+3=3x+4 or y=3x+1.