Final answer:
The sentence provided is not a run-on, but a properly constructed compound sentence that uses a comma and the coordinating conjunction 'but' to join two independent clauses with correct subject/verb agreement.
Step-by-step explanation:
The sentence "The girls played basketball, but the boys played football" is not a run-on sentence. It's a compound sentence that correctly uses a comma and the coordinating conjunction 'but' to join two independent clauses. Each clause has a subject and a verb, and the coordinating conjunction helps to show a contrast between the two actions being described.
This follows the grammatical rule that commas should be used with coordinating conjunctions when they join two independent clauses, as per the acronym FANBOYS which stands for for, and, nor, but, or, yet, so. In contrast, run-on sentences occur when independent clauses are joined without proper punctuation or a coordinating conjunction.
The sentence in question effectively communicates two separate but related actions occurring simultaneously and uses the correct subject/verb agreement for each clause.