Servus saccum gravem lente ad horreum trahit.

Because servus is in the nominative singular, which is the case typically used for the subject of a finite verb.

Also, the verb trahit is third person singular, so it matches a singular subject: servus.

So:

• servus = subject
• trahit = he drags / is dragging

Because saccum is in the accusative singular, which is the case commonly used for the direct object.

In this sentence, saccum is the thing being dragged, not the one doing the dragging.

So:

• servus = the one acting
• saccum = the thing acted on

Because adjectives in Latin must agree with the nouns they describe in:

• gender
• number
• case

But they do not have to look identical, because they may belong to different declension patterns.

Here:

• saccum is masculine, singular, accusative
• gravem is also masculine, singular, accusative

They match in grammar, even though the endings are different:

• saccum comes from a second-declension noun: saccus
• gravem comes from a third-declension adjective: gravis

So the important thing is not same ending, but same case/number/gender.

Gravem is the accusative singular masculine form of gravis, meaning heavy.

It describes saccum, so it means the heavy sack.

Because saccum is masculine singular accusative, the adjective must also be masculine singular accusative:

• gravis → nominative
• gravem → accusative

Lente is an adverb, meaning slowly.

It tells you how the action is done: the dragging happens slowly.

It is related to the adjective lentus, lenta, lentum, meaning slow.
A common pattern in Latin is:

• adjective: lentus = slow
• adverb: lente = slowly

So:

• gravem describes a noun
• lente describes the verb trahit

Because ad is a preposition meaning to or toward, and it takes the accusative case.

So:

• ad
  • accusative = movement toward something

Here, horreum is the accusative singular form.

That tells you the motion is directed toward the storehouse/granary.

Trahit is:

• present tense
• active voice
• indicative mood
• third person singular

It comes from the verb trahere, meaning to drag or to pull.

So trahit means:

• he drags
• she drags
• it drags

In this sentence, since the subject is servus, it means the slave drags.

Latin often puts the verb near or at the end of the sentence, but it does not have to.

So this order is very normal:

• Servus saccum gravem lente ad horreum trahit.

But Latin word order is more flexible than English because the endings show the grammatical roles.

For example, the following would still mean basically the same thing:

• Saccum gravem servus ad horreum lente trahit.
• Lente servus saccum gravem ad horreum trahit.

Word order in Latin often affects emphasis more than basic meaning.

Classical Latin has no articles like English the and a/an.

So servus can mean:

• a slave
• the slave

And saccum can mean:

• a sack
• the sack

Context tells you which is more natural in translation.

That is why the Latin sentence can be translated in slightly different ways in English even though the Latin stays the same.

Yes. Latin often allows either order:

• saccum gravem
• gravem saccum

Both are grammatical.

Sometimes word order gives a slight difference in emphasis, but both clearly show that gravem modifies saccum because the forms agree.

So a learner should rely more on case and agreement than on word order alone.

A good way to analyze the sentence is to reduce each word to its dictionary form:

• servus → servus, servi = slave
• saccum → saccus, sacci = sack
• gravem → gravis, grave = heavy
• lente → from lentus, lenta, lentum; adverb lente = slowly
• ad → ad = to, toward
• horreum → horreum, horrei = storehouse, granary
• trahit → traho, trahere, traxi, tractum = drag, pull

This is a very useful habit when reading Latin: identify the form in the sentence, then connect it to the dictionary entry.

Here it is accusative singular, because ad takes the accusative.

But horreum is a neuter second-declension noun, and in the neuter second declension:

• nominative singular = -um
• accusative singular = -um

So the nominative and accusative singular look the same.

That can seem strange at first, but it is completely normal for neuter nouns in Latin.