Final answer:
The word that should appear on the connecting line is 'food.'
Step-by-step explanation:
The word that should appear on the connecting line is food.
In this sentence, 'After the dance was finished, we went out for something to eat,' the phrase 'something to eat' represents the object of the verb 'went out for.' In this case, 'something' refers to food, as the purpose of going out was to find a meal after the dance. Therefore, the word 'food' is the most appropriate choice to complete the sentence.