Moji roditelji žive u gradu.

Because moji has to agree with roditelji.

• roditelji = parents
• It is masculine plural nominative
• So the possessive my must also be masculine plural nominative: moji

Compare:

• moj roditelj = my parent
• moja majka = my mother
• moje dete = my child
• moji roditelji = my parents

So moji is the correct matching form here.

It is plural.

• roditelj = parent
• roditelji = parents

In this sentence, roditelji is the subject, so it appears in the nominative plural.

Because the subject is plural: moji roditelji = my parents.

žive is the 3rd person plural present tense form of živeti / živjeti = to live.

A quick comparison:

• ja živim = I live
• ti živiš = you live
• on/ona živi = he/she lives
• mi živimo = we live
• vi živite = you (plural/formal) live
• oni/one žive = they live

Since parents = they, the verb must be žive.

Because u can take different cases depending on the meaning.

Here, the meaning is location: they live in the city/town.
For location, u takes the locative case.

• grad = city / town
• u gradu = in the city / town

If the meaning were movement toward/into something, you would use the accusative:

• Idem u grad. = I am going to town / into the city.

So:

• u gradu = in the city (location)
• u grad = into town / to town (direction)

It can mean city or town, depending on context.

So u gradu may be understood as:

• in the city
• in town

In many everyday situations, Serbian grad is broader than English city and often covers what English might call either a town or a city.

Yes.

• Roditelji žive u gradu. = The parents / parents live in the city.

But without moji, the meaning becomes less specifically my parents unless the context already makes that clear.

So:

• Moji roditelji žive u gradu. = My parents live in the city.
• Roditelji žive u gradu. = Parents / the parents live in the city.

Including moji makes the meaning explicit.

No, Serbian word order is fairly flexible.

The neutral, most straightforward order is:

• Moji roditelji žive u gradu.

But you can change the order for emphasis:

• U gradu žive moji roditelji. = It is in the city that my parents live.
• Žive moji roditelji u gradu. = possible, but less neutral and more marked

Because Serbian uses case endings, word order often expresses focus or emphasis rather than basic grammar.

No. Serbian does not have articles like English a and the.

So grad can mean:

• a city
• the city
• city/town

The exact meaning depends on context.

That is why u gradu can be translated as in the city or sometimes in town.

Here it means live/reside.

The verb živeti / živjeti can refer to:

• being alive
• living somewhere
• living a certain kind of life

In this sentence, because of u gradu = in the city, the meaning is clearly reside:

• Moji roditelji žive u gradu. = My parents live in the city.

A simple English-friendly guide is:

• Moji ≈ MOY-ee
• roditelji ≈ ro-dee-TELY-ee
  (the lj is a soft sound, similar to the lli in some pronunciations of million)
• žive ≈ ZHEE-veh
  (ž sounds like the s in measure)
• u ≈ oo
• gradu ≈ GRAH-doo

So roughly:

MOY-ee ro-dee-TELY-ee ZHEE-veh oo GRAH-doo

It is in the nominative plural, because it is the subject of the sentence.

The basic structure is:

• Moji roditelji = subject
• žive = verb
• u gradu = place expression

So:

• roditelji is nominative plural
• gradu is locative singular

Because Serbian nouns change form depending on their grammatical role and the preposition used.

The basic dictionary form is:

• grad = city/town

After u when it means in, the noun goes into the locative:

• u gradu = in the city

So the ending changes from -Ø to -u.

This is a normal masculine singular pattern in Serbian:

• u gradu = in the city
• u parku = in the park
• u stanu = in the apartment

Yes. That would mean My parents live in the village.

It follows the same pattern:

• Moji roditelji = my parents
• žive = live
• u selu = in the village

This is useful for seeing the structure:

• u gradu = in the city/town
• u selu = in the village

So the sentence pattern is very reusable.