Sjálfsafgreiðsluvélin er laus.

Because Icelandic very often builds nouns as compounds.

You can break sjálfsafgreiðsluvélin into parts like this:

• sjálfs = self-
• afgreiðslu = service/checkout, in a compound form
• vél = machine
• -in = the

So the whole word is basically self-service-machine-the.

This is completely normal in Icelandic. What English writes as several words, Icelandic often writes as one compound word.

That is a common Icelandic compounding pattern.

The noun is afgreiðsla, but when it appears inside a compound, it often uses the stem afgreiðslu- instead. Many feminine nouns ending in -a behave like this.

So:

• afgreiðsla = service, checkout
• sjálfsafgreiðsla = self-service
• sjálfsafgreiðsluvél = self-service machine

A good practical rule is: in compounds, don’t expect every noun to stay in its exact dictionary form.

It is attached to the noun as -in.

Icelandic usually puts the definite article onto the end of the noun instead of using a separate word in front.

For example:

• vél = machine
• vélin = the machine

The same thing happens in the full compound:

• sjálfsafgreiðsluvél = self-service machine
• sjálfsafgreiðsluvélin = the self-service machine

The dictionary form is sjálfsafgreiðsluvél.

The ending -in is just the definite article. If you remove it, you get the basic noun form.

Also, the head of the compound is vél, and vél is a feminine noun. That means the whole compound is feminine too.

Because adjectives in Icelandic must agree with the noun they describe in:

• gender
• number
• case

Here, sjálfsafgreiðsluvélin is:

• feminine
• singular
• nominative

So the adjective has to match that, and the correct form is laus.

Compare:

• vélin er laus = the machine is available/free
• herbergið er laust = the room is available/free
• stólarnir eru lausir = the chairs are available/free

So laus is there because it matches the noun.

Because this is a predicate adjective, not an attributive adjective.

That means:

• lausa vélin = the available/free machine
  
  • here the adjective stands directly with the noun
  • this often uses the weak form

But:

• vélin er laus = the machine is available/free
  
  • here the adjective comes after er
  • this uses the normal predicate form

So even though the noun is definite, after er you still say laus, not lausa.

Here laus means something like:

• available
• free
• not currently in use
• unoccupied

So the idea is that the machine is free for someone to use.

In other contexts, laus can also mean things like:

• loose
• unattached
• free from something

So it is a flexible word, and the exact English translation depends on context.

Er means is.

It is the 3rd person singular present form of vera, which means to be.

So:

• ég er = I am
• þú ert = you are
• hann/hún/það er = he/she/it is

Since sjálfsafgreiðsluvélin is singular, er is the correct verb form.

It is in the nominative case.

That is because it is the subject of the sentence.

The adjective laus is also nominative here, because predicate adjectives after vera normally agree with the subject and appear in the nominative as well.

So the basic structure is:

• subject in nominative
• vera
• predicate adjective in nominative

Icelandic has no separate word for a/an.

To make the noun indefinite, you simply remove the definite ending:

• Sjálfsafgreiðsluvél er laus.

That is the indefinite version.

So the contrast is:

• sjálfsafgreiðsluvél = a self-service machine / self-service machine
• sjálfsafgreiðsluvélin = the self-service machine

Context usually tells you whether the indefinite noun means a certain unspecified one or something more general.