Läraren är duktig.

Because -en is the definite ending here. Swedish often puts the at the end of the noun instead of using a separate word.

• lärare = teacher
• läraren = the teacher

So Läraren är duktig uses the definite form: the teacher.

The dictionary form is lärare.

You would usually learn the noun as:

• en lärare = a teacher

Then the forms are:

• en lärare = a teacher
• läraren = the teacher
• lärare = teachers
• lärarna = the teachers

A useful thing to notice is that lärare has the same form in singular and plural indefinite.

In Swedish, the definite article is often attached to the noun as an ending.

So instead of saying something like the teacher with a separate word before the noun, Swedish usually says:

• läraren = teacher + the

This is very normal in Swedish. English speakers often need a little time to get used to the idea that the can be built into the noun itself.

Är is the present tense of vara, which means to be.

So:

• jag är = I am
• du är = you are
• han/hon är = he/she is
• läraren är = the teacher is

Unlike English, Swedish does not change the present tense verb depending on the subject. It stays är for all persons.

Because Swedish adjectives agree with the noun in gender and number.

Here, läraren refers to one common-gender noun, so the adjective takes the basic common singular form:

• duktig

Compare:

• Läraren är duktig. = The teacher is skilled.
• Barnet är duktigt. = The child is well-behaved / good.
  (barnet is neuter, so duktigt)
• Lärarna är duktiga. = The teachers are skilled.
  (plural, so duktiga)

So duktig is the correct form for one en-word noun like lärare.

Here, duktig means something like:

• skilled
• capable
• good at what they do
• competent

It is a very common Swedish adjective, but its meaning depends on context.

For example:

• about a teacher: skilled / competent
• about a child: often good / well-behaved / clever
• about someone doing a task: good at it

So in Läraren är duktig, it usually means the teacher is good at teaching or competent.

Yes, you can, but it is not exactly the same.

• Läraren är duktig suggests the teacher is skilled / capable / competent.
• Läraren är bra means the teacher is good, but in a broader and sometimes less specific way.

Very roughly:

• duktig = good because of skill or ability
• bra = good in a general sense

In many situations, both are possible, but duktig often sounds more like praising someone's competence.

Because den läraren and läraren are not used in exactly the same way.

• läraren = the teacher in a normal, straightforward sense
• den läraren = that teacher or that particular teacher, often with extra emphasis

So if you just mean the teacher, läraren is the natural choice.

You would use den läraren more when pointing someone out or contrasting:

• Den läraren är duktig, men den andra är sträng.
  = That teacher is skilled, but the other one is strict.

A simple learner-friendly guide would be:

• Läraren ≈ LEH-ra-ren
• är ≈ air but shorter
• duktig ≈ DUK-tig

A few helpful notes:

• ä sounds somewhat like the vowel in bed, though not exactly the same.
• The stress in lärare is on the first syllable: LÄ-ra-re
• The whole sentence has a smooth rhythm: LÄ-ra-ren är DUK-tig

You do not need perfect pronunciation right away; the most important things are getting the stress roughly right and making ä clearly different from a.

Yes. This is the normal word order for a simple statement:

• subject + verb + adjective
• Läraren
  • är
    • duktig

Swedish main clauses usually follow the verb-second rule, often called V2. In this sentence, the subject comes first, so the verb comes second naturally.

You can see the same pattern in:

• Han är trött. = He is tired.
• Boken är dyr. = The book is expensive.

You usually make a yes/no question by putting the verb first:

• Är läraren duktig? = Is the teacher skilled?

So:

• statement: Läraren är duktig.
• question: Är läraren duktig?

This verb-first pattern is very common in Swedish yes/no questions.

The plural version is:

• Lärarna är duktiga. = The teachers are skilled.

Notice both changes:

• läraren → lärarna
• duktig → duktiga

That is because the noun becomes plural, and the adjective changes to match.

No. If the adjective comes before the noun, it changes form.

Compare:

• Läraren är duktig. = The teacher is skilled.
  Here duktig is a predicate adjective after är.

But:

• den duktiga läraren = the skilled teacher
  Here the adjective comes before the noun, so it becomes duktiga.

This is a very common thing for learners to notice:

• after är: duktig
• before a definite noun: duktiga

So Swedish uses different adjective forms depending on how the adjective is used in the sentence.