I am studying for a test and am confused about one point. In my book, there is one rule that states Independent, (FANBOYS) Independent. This shows the general rule that you can connect independent clauses with a comma and a coordinating conjunction. This is fine. The next rule says Independent (FANBOYS) Dependent. I am not so sure about this one. What is an example of this type of construction? The example given by the book is "I'll take the #2 with a coke but will pass on the shake." However, how is "will pass on the shake" a dependent clause? Isn't it an independent clause with an implied subject?
Most commonly, dependent clauses are subordinate clauses. Though your second clause here is a main clause, it is also a dependent clause. Here's why:
The second clause is considered to be dependent because of the coordinating conjunction but. This conjunction may coordinately link clauses, but it implies contrast. Whenever you contrast something, you need something else to contrast it to.
So, to contrast the second clause, you need the first clause, therefore the second clause is dependent. If you invert the order of the two clauses you'll also find that that does not work. You need the first clause first in order for the second one to be valid. If you swap the order of the clauses while keeping but in between of them you'll alter the meaning.
About the subject in the second clause: The subject is the same as the one in the first clause, which is why it was elided in the second one.
Now, do dependent clauses have to have subjects? Normally, all clauses need subjects, with the exception of non-finite clauses (they can refer to the subject in the clause to which they are linked). However, non-expressed subjects are still subjects, so the second clause in your example sentence does actually contain a subject even though you cannot see it.