A despesa variável faz parte do custo de vida.

A is the feminine singular definite article, meaning the.

It is used here because despesa is a feminine singular noun:

• a despesa = the expense
• as despesas = the expenses

In Portuguese, articles are often used more often than in English. So even when English might say something more general like Variable expense is part of the cost of living, Portuguese often prefers A despesa variável...

Here, a despesa variável can mean:

• the variable expense
• or more generally, variable expense as a category

Yes, despesa is feminine.

You usually learn the gender together with the noun:

• a despesa
• a casa
• a comida

Many nouns ending in -a are feminine, though not all. The safest habit is to memorize the noun with its article.

Because despesa is feminine singular, the article is a and any adjective describing it must also match in gender/number when possible.

Both are related to money, but they are not exactly the same.

• despesa = an expense, something you spend money on
• custo = a cost, the amount something costs

So:

• despesas are your bills, expenses, outgoings
• custo de vida is the cost of living

In this sentence:

• despesa variável = a variable expense
• custo de vida = cost of living

A simple way to remember it:

• despesa is usually from the spender’s point of view
• custo is usually the price or cost itself

In Portuguese, adjectives often come after the noun.

So:

• despesa variável = variable expense
• custo fixo = fixed cost
• mercado financeiro = financial market

Putting the adjective after the noun is the most normal order here. In some cases, Portuguese adjectives can go before the noun, but that often changes the tone or meaning. With variável, the standard order is despesa variável.

Not all Portuguese adjectives change form for masculine/feminine.

Variável is an adjective with the same form for both masculine and feminine singular:

• custo variável
• despesa variável

But it does change in the plural:

• custos variáveis
• despesas variáveis

So the agreement is still there, but in the singular, masculine and feminine happen to look the same.

Fazer parte de means to be part of.

So:

• faz parte de = is part of
• literally, it comes from fazer
  • parte, but you should learn the whole expression as a set phrase

Examples:

• Isso faz parte do trabalho. = That is part of the job.
• Ela faz parte da equipe. = She is part of the team.

In your sentence:

• A despesa variável faz parte do custo de vida. = Variable expense is part of the cost of living.

Because faz is the conjugated form of the verb fazer.

The subject is A despesa variável, which is third-person singular, so the verb must also be third-person singular:

• eu faço
• você faz
• ele/ela faz
• a despesa faz

So:

• A despesa variável faz parte... not
• A despesa variável fazer parte...

Because in Portuguese, de + o contracts to do.

So:

• de + o = do
• de + a = da
• de + os = dos
• de + as = das

That means:

• faz parte do custo = is part of the cost
• literally: faz parte de o custo → contracted to do custo

This kind of contraction is very common and important in Portuguese.

Custo de vida is the standard fixed expression for cost of living.

Here, de vida works like of living in a general sense, not of the life.

Compare:

• custo de vida = cost of living
• qualidade de vida = quality of life
• estilo de vida = lifestyle / style of life

If you said custo da vida, it would usually sound like the cost of life in a more specific or unusual sense, not the normal economic expression.

So this is something worth learning as a chunk:

• custo de vida

Yes. A very natural plural version would be:

• As despesas variáveis fazem parte do custo de vida.

Changes:

• A → As
• despesa → despesas
• variável → variáveis
• faz → fazem

This version may feel even more natural in some contexts, because people often talk about variable expenses in the plural.

Sometimes yes, but they are not always exactly interchangeable.

• despesa is very common in financial, accounting, and budgeting language
• gasto is also common and often sounds a bit more everyday, like spending or expense

Depending on context, both can work:

• despesa variável
• gasto variável

But despesa variável sounds especially natural in budgeting, personal finance, or formal financial discussion.

It can often be understood as the general concept.

In Portuguese, the singular with a definite article is often used to talk about a whole category:

• A despesa variável = Variable expense / A variable expense category
• O café é popular no Brasil. = Coffee is popular in Brazil.

So even though it is singular, it does not have to mean one single specific expense. Context decides that.

In Brazilian Portuguese, variável is pronounced approximately like:

vah-ree-AH-vel

A few notes:

• the stress falls on á: variável
• the ending -vel is not pronounced like English veil
• the r in variável is usually a softer Brazilian r sound between vowels

And despesa is approximately:

des-PEH-zah

with the stress on pe:

• despesa

Here is a quick breakdown:

• A = the (feminine singular article)
• despesa = expense
• variável = variable
• faz = does / makes, but in the expression faz parte de, it means is part of
• parte = part
• do = of the (de + o)
• custo = cost
• de vida = of living

So the structure is:

A despesa variável
(subject)

faz parte do custo de vida
(predicate: is part of the cost of living)