Vid den första kassan är kön lång, så vi går till en annan kassa.

Because Swedish main clauses usually follow the V2 rule: the finite verb comes in the second position.

Here, Vid den första kassan is placed first for emphasis or setting the scene, so the verb är must come next:

• Vid den första kassan är kön lång.

If you started with the subject instead, you would get:

• Kön är lång vid den första kassan.

Both are grammatical, but the sentence you were given highlights the location first.

So this is not a question word order. It is normal Swedish statement word order after fronting a phrase.

Vid here means something like at, by, or near.

So vid den första kassan means at the first checkout / by the first cash register.

It is a very common preposition when talking about being positioned next to some place or point:

• vid dörren = by the door
• vid bordet = at the table
• vid kassan = at the checkout

In this sentence, vid is the natural choice for talking about the line at a particular checkout.

Because Swedish usually uses double definiteness when a definite noun has an adjective or similar modifier before it.

That means you often get:

• a definite article before the adjective: den
• and a definite ending on the noun: -an

So:

• den första kassan = the first checkout

Compare:

• kassan = the checkout
• den första kassan = the first checkout

This is very normal in Swedish:

• den stora bilen = the big car
• det röda huset = the red house
• de gamla böckerna = the old books

Also, första is the ordinal first, and it stays första here.

Here kassa means checkout, cash register, or till, depending on the context and the variety of English.

In a supermarket, kassa often refers to the place where you pay, not just the machine itself.

So:

• en kassa = a checkout / a till / a cash register
• kassan = the checkout / the till

In this sentence, it clearly means the checkout area in a store.

Yes, and that can definitely confuse learners.

There are two different words involved:

• en kö = a queue, a line
• ett kön = a sex / gender

In your sentence, kön is the definite form of en kö:

• en kö = a queue
• kön = the queue

So:

• kön är lång = the queue is long

This has nothing to do with gender here; only the context tells you which word it is.

Yes. En lång kö / kön är lång is the normal way to say that a queue is long.

Swedish often describes the queue itself:

• Det är en lång kö. = There is a long queue.
• Kön är lång. = The queue is long.

Both are possible, but in this sentence kön is treated as a specific, visible queue at that checkout, so the definite form feels natural.

English sometimes prefers there is a long line, while Swedish is very happy with the queue is long.

Så here means so or therefore.

It links the two parts of the sentence:

• Vid den första kassan är kön lång = At the first checkout, the queue is long
• så vi går till en annan kassa = so we go to another checkout

It shows that the second action happens because of the first situation.

This is very common in everyday Swedish.

Går is the present tense of gå, which literally means walk, but in many everyday situations it can also mean go.

So vi går till en annan kassa can mean:

• we go to another checkout
• we walk over to another checkout

The preposition till means to, showing movement toward a destination.

So:

• gå till = go to / walk to

In a shop context, this sounds completely natural.

Because en annan kassa means another checkout or a different checkout, while den andra kassan means the other checkout or the second checkout.

So the sentence is saying:

• not this checkout
• let’s go to some other one

That is why en annan kassa fits best.

Compare:

• en annan kassa = another checkout / a different checkout
• den andra kassan = the other checkout / the second checkout

Also note the pattern:

• en annan with an en-word
• ett annat with an ett-word

For example:

• en annan butik = another shop
• ett annat bord = another table

Yes. Swedish allows a few natural variations. For example:

• Kön är lång vid den första kassan, så vi går till en annan kassa.
• Det är lång kö vid den första kassan, så vi går till en annan kassa.

These all express basically the same idea, but the original sentence puts the location first:

• Vid den första kassan ...

That makes the sentence sound slightly more focused on where the problem is.