From what your saying did you want to make sure pt. 5s' x value becomes 0, while at the same time overall having some control of the lines shape with a ramp?
If so, this does it. And because I am using a B-spline controls like you used, it's necessary to put additional control handles on each side of the target control that is going to be for your pt that you want to make sure is 0.
This way with the fit functions you don't have to ‘fiddle’ around and manually bring it to 0.
Also while being able to transform the whole line to any value - while pt.5s' x value remains 0.