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Please give me a hand to figure out this problem !!!

This sentence from my homework finding the mistakes in the sentence.

Some methods to prevent soil erosion are plowing parallel with the slopes of hills to plant trees on unproductive land, and rotating crops.

- "to prevent soil erosion" is an adjective phrase modifying the noun "methods"
- "to plant trees" is the mistake in this sentence. I have changed it to "planting"

My question is what the role of "TO" in "to prevent soil erosion" is.

There is another example, "Can you tell me the way to solve this problem?"

So what is "TO"?

Is it the Preposition? I have learned that after Preposition, we usually have a Noun, a Pronoun or a Gerund. Is it the reason why "TO" is an exception because we just use TO before the Verb Bare Infinitive?

Is there any difference between
Some methods OF preventing soil erosion...
&
Some methods TO prevent soil erosion ...

Thanks for your attention.

AnnaLaker wrote: Is there any difference between
Some methods OF preventing soil erosion...
&
Some methods TO prevent soil erosion ...

They are simply different structures with exactly the same meaning.

'Of' functions here as a normal preposition (cf. method of NP), and is therefore followed by a gerund. 'To' here simply precedes the infinitive (i.e. there is no such collocation as *method to NP) .

The possibility of postmodifying a noun by means of an infinitive as well as, or possibly even instead of, a prepositional phrase depends very much on the noun in question, although there are a number of common cases similar to the above (chance to do/chance of doing, etc.)

A good learners' dictionary (e.g. the Collins Cobuild) will always carry this kind of information.