Final answer:
A compound sentence composed of two independent clauses joined by the conjunction 'but', expresses a contrast between willingness to go and the need to rest because of tiredness.
Step-by-step explanation:
The sentence "I would go with you but I am tired and just want to go to bed." is a compound sentence. This type of sentence is made up of two independent clauses connected by the coordinating conjunction 'but'. The first clause, 'I would go with you', could stand alone as a complete sentence, as could the second clause, 'I am tired and just want to go to bed'. Each clause expresses a complete thought, and the use of the conjunction 'but' shows a contrast between wanting to accompany someone and the need to rest due to tiredness.