Answer:
Medicine prescriptions must be written in ink because doctors (or whoever has prescribed the medicine) can not always trust that a patient will not erase the pencil and rewrite the prescription as something else like an addicting drug. Some patients are not to be trusted and that could get the doctor (or medical professional) to get into a lot of legal trouble. Pen prevents this from happening and also looks much more formal on a document of pharmaceutical slip.
I hope this helps! :D