Magistra veritati favet et discipulis rationem clare explicat.

Because magistra is the subject of the sentence: it is the person doing the actions.

Here, the teacher is doing both actions:

• favet = favors
• explicat = explains

So magistra must be in the nominative singular.

Because faveo takes the dative, not the accusative.

In English, we say favor truth, where truth looks like a direct object. But in Latin, faveo means something more like show favor to or be favorable to, so the thing favored goes into the dative case.

So:

• veritas = truth
• veritati = to truth / toward truth

This is a very common thing to learn in Latin: some verbs take cases that do not match English expectations.

Because discipulis is the indirect object with explicat.

The sentence means that the teacher explains rationem to the students.

So:

• rationem = the thing being explained → direct object → accusative
• discipulis = the people receiving the explanation → indirect object → dative

This works much like English to the students, except Latin often uses the dative without needing a separate word for to.

Rationem is accusative singular.

It is the direct object of explicat, because it is the thing being explained.

Basic structure:

• magistra = subject
• explicat = verb
• rationem = direct object
• discipulis = indirect object

Also, rationem comes from the noun ratio, rationis.

Clare is an adverb, meaning clearly.

It modifies the verb explicat, telling us how the teacher explains:

• explicat = explains
• clare explicat = explains clearly

A learner may notice that many Latin adverbs are formed from adjectives. Here:

• clarus, clara, clarum = clear / bright / famous
• clare = clearly

Because the same subject applies to both verbs.

The structure is:

• Magistra veritati favet
• et discipulis rationem clare explicat

Latin, like English, does not need to repeat the subject if it stays the same.

So the sentence means:

• The teacher favors truth
• and explains the matter clearly to the students

with magistra understood as the subject of both favet and explicat.

Both are 3rd person singular present active indicative.

That means:

• 3rd person singular = he/she/it
• present = happening now or generally true
• active = the subject performs the action
• indicative = ordinary statement of fact

So:

• favet = she favors / the teacher favors
• explicat = she explains / the teacher explains

Because magistra is singular, the verbs are singular too.

Yes. Latin word order is much more flexible than English word order because the endings show the grammatical roles.

For example, the sentence could be rearranged in various ways without changing the basic meaning, such as:

• Magistra discipulis rationem clare explicat et veritati favet.
• Veritati magistra favet et rationem discipulis clare explicat.

The original order is perfectly natural, but the endings tell you:

• magistra = subject
• veritati = dative with favet
• discipulis = indirect object
• rationem = direct object

So Latin does not rely as heavily on position as English does.

It can, but ratio is a very flexible word.

Depending on context, ratio can mean:

• reason
• explanation
• plan
• method
• system
• account

So rationem explicat could be understood as:

• explains the reason
• explains the principle
• explains the method
• gives an explanation

The exact English translation depends on context. A learner should not assume Latin nouns always have just one fixed English equivalent.

Grammatically, magistra is a feminine noun, and it normally means a female teacher or mistress in older usage.

So yes, in ordinary reading, this would usually refer to a woman.

Compare:

• magister = male teacher
• magistra = female teacher

This is a matter of the noun itself, not just the sentence structure.

A learner might look them up as follows:

• magistra → magistra, magistrae
• veritati → veritas, veritatis
• favet → faveo, favere, favi, fautum
• discipulis → discipulus, discipuli
• rationem → ratio, rationis
• clare → from clarus, clara, clarum or listed as clare
• explicat → explico, explicare, explicavi, explicatum

Knowing the dictionary form is important because many forms in the sentence are inflected and do not look exactly like the headword.

The cases and the verb meanings help you match them up.

You can group the sentence like this:

• Magistra → the subject
• veritati favet → favors truth
• discipulis rationem clare explicat → explains the matter clearly to the students

More specifically:

• veritati goes with favet because faveo takes the dative
• rationem goes with explicat as its direct object
• discipulis goes with explicat as the indirect object
• clare goes with explicat as an adverb

This is an important Latin reading skill: you do not just read left to right mechanically; you use endings and verb patterns to see the structure.