Learn Finnish: Hengitän hiljaa, jotta ääneni ei vapise. - I breathe quietly so that my voice does not tremble.

While both can translate to "that" in English, jotta specifically expresses purpose, meaning "so that" or "in order to". Että is a neutral "that" used simply to connect clauses (like "I think that...").

What case is ääneni in here?

It is in the basic nominative case. It consists of the base word ääni (voice) plus the first-person possessive suffix -ni (my). It is in the nominative because it acts as the subject of the second clause.

Where does the word vapise come from?

It is the negative present form of the verb vapista (to tremble or shake), which is a Type 4 verb. To find the negative stem for any verb, you take the "I" form (vapisen) and drop the -n, giving you ei vapise.

Wait, doesn't hiljaa mean "slowly"?

It can mean both! In Finnish, hiljaa is used for doing things at a low volume (quietly) as well as at a low speed (slowly). The context tells you which one makes the most sense.