هذا نبات منزلي.

هذا means this for a masculine singular noun.

In this sentence, the thing being pointed out is نبات (plant), which is grammatically masculine in Arabic, so هذا is the correct form.

Compare:

• هذا = this (masculine)
• هذه = this (feminine)

So if the noun were feminine, you would use هذه instead.

In Arabic, the verb to be in the present tense is usually not written or said.

So:

• هذا نبات منزلي. literally looks like:
• This houseplant but it means:
• This is a houseplant.

This is completely normal in Arabic nominal sentences.

Because the sentence means This is a houseplant, not This is the houseplant.

In Arabic, when the predicate is indefinite in English (a plant, a book, a teacher), it is usually indefinite in Arabic too.

So:

• نبات = a plant / plant
• النبات = the plant

If you said هذا النبات المنزلي, that would mean this houseplant or this indoor plant, not this is a houseplant.

Yes. Here منزلي is an adjective describing نبات.

It means something like:

• domestic
• household
• home/indoor

So نبات منزلي means a houseplant or an indoor plant.

The -ي here is part of a very common Arabic adjective pattern called the nisba pattern.

It often turns a noun into an adjective meaning related to that noun.

For example:

• منزل = home / house
• منزلي = home-related, domestic, household

So منزلي here does not mean my home. It is an adjective meaning domestic / household / home-type.

Yes, in writing without vowels, it can look the same.

• منزلي can mean my house/home
• منزلي can also be the adjective domestic / household

The context tells you which meaning is intended.

In هذا نبات منزلي, the adjective meaning is the natural one, because it is describing نبات.

Because it is describing نبات, and نبات is grammatically masculine singular.

Arabic adjectives usually agree with the nouns they describe in:

• gender
• number
• definiteness
• case

So here:

• نبات = masculine singular, indefinite
• منزلي = masculine singular, indefinite

That is why the adjective appears in this form.

Then both the demonstrative and the adjective would change.

For example, if you used نبتة (a plant, feminine), you would say:

• هذه نبتة منزلية.

Here:

• هذه = this (feminine)
• منزلية = feminine form of منزلي

So Arabic makes the agreement very visible.

A careful full pronunciation would be roughly:

hādhā nabātun manziliyyun

In normal pause, many speakers would say something closer to:

hādhā nabāt manzilī

A few notes:

• هذا = hādhā
• نبات = nabāt
• منزلي = manzilī (or manziliyyun with full case ending in careful reading)

Yes. In fully vocalized formal Arabic, the sentence would usually be written with case endings as:

هٰذا نَباتٌ مَنْزِلِيٌّ

Both نباتٌ and منزليٌّ are in the nominative here.

But in everyday Arabic writing, those short vowels and tanwīn are usually omitted, so you normally see:

هذا نبات منزلي

A simple learner-friendly way to understand it is:

• هذا = this
• نبات منزلي = a houseplant

So the whole structure is:

• This
  • a houseplant

Arabic often builds present-tense sentences this way, without using a separate word for is.

They mean different things.

• هذا نبات منزلي = This is a houseplant
• هذا النبات المنزلي = This houseplant / This indoor plant

So the first is a full sentence. The second is a noun phrase.

That difference depends mainly on whether the noun and adjective are indefinite or definite.