Multiply and divide dates
Slope is a numeric concept.  It does not make sense to have a slope with time unless you already have a unit for it.  Fortunately we have date arithmetic in Oracle that can help you out.  To do this you need to convert to a numeric quantity as you have noted.

Date arithmetic works with addition and subtraction and this can create scoped numeric representations of this for your purposes.  Slope is easy enough (no modifications there since you are subtracting dates first).  The intercept is more interesting.  The question is at what date x = 0 is at.  If you subtract that date from x1, then you will get a numeric result that you can use for your multiplication factor.