Auf der letzten Folie sieht man eine Grafik über vegane Ernährung; dabei nennt die Dozentin auch Himbeeren und Blaubeeren als Beispiel.

Auf der letzten Folie means on the last slide.

German often puts a time, place, or context phrase at the beginning of the sentence to set the scene. Here, the sentence first tells you where something is being seen: on the last slide.

Also, German usually uses auf with things like slides, pages, posters, and screens:

• auf der Folie = on the slide
• auf der Seite = on the page
• auf dem Bildschirm = on the screen

So this opening phrase is completely natural.

Because auf here is followed by the dative case.

In this sentence, auf describes a location, not movement:

• Auf der letzten Folie = on the last slide

When auf shows location, it takes the dative:

• die Folie → der Folie in dative
• die letzte Folie → der letzten Folie

Compare:

• auf der Folie = on the slide, already there
• auf die Folie = onto the slide, movement toward it

So der letzten Folie is correct because the graphic is located there.

Because German main clauses follow the verb-second rule.

The first position in the sentence is taken by Auf der letzten Folie. Once that happens, the conjugated verb must come next:

• Auf der letzten Folie sieht man ...

If there were no opening phrase, you could say:

• Man sieht auf der letzten Folie ...

Both are correct, but the word order changes because German wants the finite verb in the second position.

Man in German is an indefinite pronoun. It often means:

• one
• you
• people
• someone, depending on context

So sieht man here means something like:

• you can see
• one can see
• people can see

In natural English, you can see is usually the best translation.

It does not mean man as in an adult male.

This phrase means a graphic/chart about vegan nutrition or a graphic about a vegan diet.

A few grammar points are happening here:

• eine Grafik is in the accusative because it is the thing being seen.
• Grafik is feminine, so the article is eine.
• über here means about / concerning.
• vegane Ernährung means vegan nutrition or vegan diet.

Also notice:

• vegane is lowercase because it is an adjective.
• Ernährung is capitalized because all German nouns are capitalized.

Here dabei means something like:

• while doing so
• in the process
• at the same time
• in that context

So:

• dabei nennt die Dozentin auch ...
  means
• while doing that / in that context, the lecturer also mentions ...

It connects the second part to the first part. The idea is:

1. There is a graphic on the last slide.
2. While discussing that graphic, the lecturer also mentions raspberries and blueberries.

So dabei is not just about time; it also links actions within the same situation.

For the same reason as sieht man earlier: German uses verb-second word order in main clauses.

The first position is occupied by dabei, so the verb comes next:

• Dabei nennt die Dozentin ...

Without dabei, you could say:

• Die Dozentin nennt auch Himbeeren und Blaubeeren als Beispiel.

But once dabei is moved to the front, the verb must stay in second position.

Because they are being mentioned as example items, not as specific, already identified berries.

So German naturally says:

• Sie nennt Himbeeren und Blaubeeren als Beispiel.

This is similar to English:

• She mentions raspberries and blueberries as an example.

You do not need articles here because the sentence is referring to the categories in a general way.

If you added articles, the meaning would become more specific:

• die Himbeeren = the raspberries
• die Blaubeeren = the blueberries

That would sound like particular berries already known from the context.

Als Beispiel means as an example.

This is a very common German expression:

• etwas als Beispiel nennen = to mention something as an example
• X als Y = X as Y

Examples:

• Ich nehme Berlin als Beispiel. = I’ll use Berlin as an example.
• Sie bezeichnet ihn als Experten. = She describes him as an expert.

So als is the normal word used to show the role or function something has.

Dozentin means a female lecturer or female instructor, usually in a university or adult-education context.

Related words:

• der Dozent = male lecturer
• die Dozentin = female lecturer

It is different from:

• die Lehrerin = school teacher
• die Professorin = professor

So Dozentin suggests someone teaching, especially in higher education, but not necessarily a professor.

The semicolon links two closely related main clauses:

1. Auf der letzten Folie sieht man eine Grafik über vegane Ernährung
2. dabei nennt die Dozentin auch Himbeeren und Blaubeeren als Beispiel

A semicolon is stronger than a comma but softer than a full stop. It shows that the two parts belong very closely together.

You could also write:

• Auf der letzten Folie sieht man eine Grafik über vegane Ernährung. Dabei nennt die Dozentin auch Himbeeren und Blaubeeren als Beispiel.

That would also be correct.

So the semicolon is mostly a punctuation/style choice here, not a special grammar requirement.