Japanese question

I'm learning the grammar of adjectives, and it seems strange to me that when you want to say that it is not a spacious house (in informal), there is no verb and that it has to be conjugated from the adjective and not from the verb, for example 広くない家, why if you want to say informally you don't have to use the verb? Is the same thing happening with 広い家? If you can explain this to me and you know When if you use the verb I would greatly appreciate it, thanks in advance.