"I study the Latin language."
Translation:Linguae Latinae studeo.
Verbs themselves can't be dative, but they can make their object be in the dative case. The verb
studere means "to dedicate oneself to/to be eager for/to busy oneself with", which is why "linguae Latinae" is in the dative case.
studeo is just the "ego" conjugation of "studere".
"Dative" comes from "dare", "to give".
Here is a plain-English overview of what the cases are and how they work:
Latin cases, in English
Adjectives must agree in gender, number, and case with the nouns they modify, but they have their own declensions. Sometimes you get lucky and the adjective just happens to follow the same declension as the noun, but that is not a guarantee.
If you're replying to someone, could you please reply directly to their comment instead of making a new top-level comment? This breaks up conversations and makes them hard to follow.
Lingua latina is nomanitive, linguam latinam is accusative, and linguae latinae is dative?
Yes. Nominative is the case for the subject or the complement, accusative is the case for the direct object (among other uses), and dative is the case for the indirect object (generally).