Learn Finnish: Tämä ohjelma on hidas testata ilman opettajaa. - This program is slow to test without a teacher.

Because it directly describes a specific, concrete subject: Tämä ohjelma (This program). If the sentence described the abstract action instead of the noun—like "It is slow to test this program"—the adjective would take the partitive: On hidasta testata tämä ohjelma.

Why do we use the basic dictionary form testata here?

This sentence uses an evaluative structure: "to be" + Adjective + Verb. In Finnish, the verb in this specific pattern takes the 1st infinitive (the basic dictionary form), neatly matching the English structure "is slow to test".

Why is opettaja (teacher) in the partitive case (opettajaa)?

The word ilman (without) is a preposition that strictly dictates the case of the noun following it. It always requires the partitive case, turning opettaja into opettajaa.

If I wanted to say "Testing this program is slow" instead, how would the sentence change?

You would shift the grammatical focus to the action of testing, which requires the partitive adjective hidasta. The sentence would become Tätä ohjelmaa on hidasta testata, where the program is now the object of the verb testata, so it also takes the partitive.