Which table gets the FK? Is there a clear Parent-Child relationship here?
If the business requirement is

a business rule, every part must belong to exactly one product line.

So if the rule is, each part belongs to one product line the other side of that relationship is each product line contains zero-to-many parts which should convince you this is a clear instance of a parent/child relationship.
How a something exists in the real world versus how it exists within a business context/database are not always strongly tied.  If I have a part on my desk I do not care about it's product line.  But if I'm a business and I am selling the part I will probably need to categorize that part for search/reporting/sales/commission purposes.
The other columns you will probably need FKs on (PartType, Grade, Family, PopularityCode, UnitClass) will have the same physical implementation (parent table, foreign key reference) even if the context might not be the same (Each Part is described by One Part Type/PartType describes zero-to-many Parts, etc).
Won't get into the column types or other aspects of the design because that's not pertinent to the question but I'll be happy to provide guidance elsewhere.