Aksamit jest drogi.

Because drogi has to agree with aksamit in gender, number, and case.

• aksamit is a masculine singular noun
• the subject is in the nominative
• so the adjective also appears in the masculine singular nominative form: drogi

Compare:

• ten aksamit jest drogi — this velvet is expensive
• ta tkanina jest droga — this fabric is expensive
• to krzesło jest drogie — this chair is expensive

So the ending changes depending on the noun.

Yes. Aksamit is masculine singular.

You can see this from agreement:

• ten aksamit
• drogi aksamit
• aksamit jest drogi

Even though velvet is not naturally male or female, Polish still assigns every noun a grammatical gender.

It is in the nominative case because it is the subject of the sentence.

In Aksamit jest drogi:

• aksamit = subject
• jest = verb
• drogi = adjective describing the subject

The adjective is also nominative because it agrees with the subject in this kind of sentence.

In normal standard Polish, jest is needed in the present tense.

• Aksamit jest drogi — normal, neutral Polish

Without jest:

• Aksamit drogi — sounds incomplete, poetic, stylistic, or like a note/headline rather than an ordinary sentence

So for a learner, the safe rule is: in standard present-tense statements like this, use jest.

In ordinary sentences with być (to be), yes.

Examples:

• On jest zmęczony — He is tired
• To jest trudne — This is difficult
• Aksamit jest drogi — Velvet is expensive

This is different from some other Slavic languages where the present-tense to be may be omitted more often.

Because Polish does not have articles like English a/an and the.

So Aksamit jest drogi could mean, depending on context:

• Velvet is expensive
• The velvet is expensive

Context tells you which meaning is intended.

Yes. Drogi can mean both:

• expensive
• dear / beloved

For example:

• To jest drogie auto — This is an expensive car
• Mój drogi przyjaciel — My dear friend

In Aksamit jest drogi, the meaning is clearly expensive, not dear.

The dictionary forms are:

• aksamit — velvet
• być — to be
• drogi — expensive / dear

Here, jest is the 3rd person singular present form of być.

A simple pronunciation guide:

• Aksamit ≈ ak-SA-meet
• jest ≈ yest
• drogi ≈ DRO-ghee

A few useful notes:

• Polish j sounds like English y in yes
• Polish g is always a hard g, like in go
• stress usually falls on the second-to-last syllable:
  • akSAmit
  • jest
  • DROgi

Yes, Polish word order is more flexible than English, although Aksamit jest drogi is the most neutral order.

Possible variations include:

• Drogi jest aksamit
• Jest drogi aksamit

But these sound marked, poetic, or focused in some special way. For everyday use, stick with:

• Aksamit jest drogi

Yes, that is also correct, but it is a slightly different structure.

• Aksamit jest drogi — Velvet is expensive
• Aksamit to drogi materiał — Velvet is an expensive material

In the second sentence, to helps identify or classify something: X is Y in the sense of X is a Y.

So both are correct, but they are not exactly the same sentence type.

Because with być plus an adjective describing the subject, Polish normally uses the nominative.

So:

• Aksamit jest drogi
• Dom jest duży
• Kawa jest zimna

The instrumental is more common when the complement is a noun, especially in many contexts:

• On jest lekarzem — He is a doctor

So here, since drogi is an adjective describing aksamit, nominative is the normal form.

Only because it is at the beginning of the sentence.

Normally the common noun is written:

• aksamit

So:

• Aksamit jest drogi. — capitalized because it starts the sentence
• Lubię aksamit. — lowercase in the middle of a sentence

If it were a brand name or proper noun, capitalization rules would be different, but here it is just the ordinary noun velvet.