Matkatavara jäi lentokentälle, joten ostin uuden hammasharjan.

Finnish often uses jäädä to express that something remained somewhere or got left behind. So matkatavara jäi lentokentälle means the baggage ended up staying at the airport. This sounds natural for an accidental situation.

A passive of jättää would sound more active or deliberate: Matkatavara jätettiin lentokentälle = The baggage was left at the airport.

Jäi is the past tense, 3rd person singular of jäädä.

• jäädä = to remain, stay behind, be left behind
• jäi = remained, stayed behind, was left behind

It is singular because the subject matkatavara is singular.

-lle is the allative ending. In this sentence, Finnish uses lentokentälle as the natural expression for the place where the baggage ended up being left behind.

Even though English says at the airport, Finnish cases do not match English prepositions exactly. So the best way to learn this is as a pattern: jäädä + place = be left/stay behind somewhere.

Because the verb ending already tells you the subject.

• ostin = I bought
• the ending -n marks 1st person singular

So minä is not necessary unless you want extra emphasis:

• Ostin uuden hammasharjan = I bought a new toothbrush
• Minä ostin uuden hammasharjan = I bought a new toothbrush

Ostin is the past tense, 1st person singular of ostaa.

• ostaa = to buy
• ostin = I bought

So the second clause literally has the verb form built into it: bought-I.

Because hammasharjan is the object of ostin, and here the buying is seen as a completed whole action: one whole toothbrush was bought.

In this kind of sentence, Finnish uses the total object. In the singular, that usually looks like the genitive form:

• hammasharja → hammasharjan

So:

• ostin uuden hammasharjan = I bought a new toothbrush

Using uusi hammasharja here would leave the noun in the nominative, which is not the normal form for this object.

Because adjectives in Finnish agree with the nouns they describe.

Since hammasharjan is in the total-object/genitive-looking form, uusi must match it:

• uusi hammasharja
• uuden hammasharjan

Both the adjective and the noun change together.

Joten means so, therefore, or as a result. It introduces the consequence of the first clause.

So the logic is:

• the baggage was left at the airport
• so I bought a new toothbrush

It is not the same as because. Joten introduces the result, not the cause.

Because joten joins two full clauses:

• Matkatavara jäi lentokentälle
• ostin uuden hammasharjan

In Finnish, a comma is normally used before this kind of conjunction.

Yes. It is a compound:

• hammas = tooth
• harja = brush

So hammasharja literally means tooth-brush, or toothbrush. Finnish uses compound words very often, and they are usually written as one word.

Yes. That would also be correct.

The difference is mainly in how you view the baggage:

• Matkatavara jäi lentokentälle = the baggage/luggage as one whole
• Matkatavarat jäivät lentokentälle = the bags/items as separate things

Both are natural, depending on what you want to emphasize.

Because Finnish has no articles. There is no direct equivalent of English a/an or the.

So Finnish uses context instead:

• matkatavara can mean baggage or the baggage
• uuden hammasharjan can mean a new toothbrush or the new toothbrush, depending on context

Yes, Finnish word order is fairly flexible, but the original sentence is the most neutral way to say it.

For example, you could also say:

Koska matkatavara jäi lentokentälle, ostin uuden hammasharjan.

That means Because the baggage was left at the airport, I bought a new toothbrush.

If you keep joten, it normally comes between the two clauses as in the original sentence.