Agricolae vetus iugum est, sed novum lorum emere vult, quia aratrum grave est.

Here agricolae is dative singular, not nominative.

Latin often uses the pattern:

X dativus + est = X has ...

So:

• Agricolae vetus iugum est literally means something like To the farmer there is an old yoke
• more naturally in English: The farmer has an old yoke

This is called the dative of possession.

Also, agricola is a first-declension noun, but it is masculine, which is something English-speaking learners often have to get used to.

Yes, agricolae can have more than one meaning by form alone:

• genitive singular = of the farmer
• dative singular = to/for the farmer
• nominative plural = farmers

But in this sentence, only the dative singular makes sense.

Why?

• agricolae vetus iugum est works well as The farmer has an old yoke
• of the farmer an old yoke is does not really form a normal sentence here
• farmers an old yoke is also does not make sense

So context tells us that agricolae is dative singular.

Latin can express possession in two common ways:

• agricola iugum habet = the farmer has a yoke
• agricolae iugum est = literally to the farmer there is a yoke

Both are possible, but the sentence you were given uses the second pattern, the dative of possession.

A learner should recognize both:

• habet = direct, straightforward has
• dative + est = another very common Latin way to say has

All three are neuter singular nouns of the second declension.

In this sentence:

• iugum is nominative singular because it is the thing that is
• lorum is accusative singular because it is the object of emere (to buy)
• aratrum is nominative singular because it is the thing that is heavy

Since these are neuter second-declension nouns, both the nominative singular and accusative singular end in -um, so you have to tell the case from the noun’s job in the sentence.

Because vetus is not a regular first-and-second-declension adjective like novus, -a, -um.

It is a third-declension adjective.

Its forms are different:

• masculine/feminine nominative singular: vetus
• neuter nominative singular: vetus
• neuter accusative singular: vetus

So with iugum (a neuter singular noun), the correct form is still vetus.

That is why:

• vetus iugum = an old yoke

not vetum iugum.

Because novum must agree with lorum in:

• gender
• number
• case

Lorum is:

• neuter
• singular
• accusative here

So the adjective novus, nova, novum must also be neuter singular accusative, which is novum.

That is standard adjective agreement in Latin.

Because aratrum is neuter singular, and the adjective gravis, grave has a special neuter form.

For this adjective:

• masculine/feminine nominative singular: gravis
• neuter nominative singular: grave

So:

• aratrum grave est = the plough is heavy

Since aratrum is neuter, grave is the correct form.

Because it depends on vult.

Vult means he wants, and Latin commonly uses an infinitive after verbs like want, be able, ought, begin, and so on.

So:

• emere = to buy
• vult emere = he wants to buy

This is called a complementary infinitive.

The subject is understood from the context: the farmer.

Latin often leaves subject pronouns unstated when the verb ending already shows the person.

• vult = he/she/it wants

Since the sentence has already mentioned the farmer, we naturally understand:

• sed novum lorum emere vult = but he wants to buy a new strap

Latin does this all the time.

Because classical Latin does not have articles like English a/an/the.

So a noun like lorum can mean, depending on context:

• a strap
• the strap
• just strap in a general sense

The same applies to iugum and aratrum.

English has to choose an article when translating, but Latin does not.

Quia means because and introduces a reason.

So:

• quia aratrum grave est = because the plough is heavy

The clause after quia explains why he wants to buy the new strap.

Latin word order is much more flexible than English word order because the endings show how words function.

English depends heavily on position:

• The farmer buys the strap

Latin can move words around more freely because case endings and verb forms carry a lot of the grammar.

In this sentence, the order is:

• Agricolae vetus iugum est
• sed novum lorum emere vult
• quia aratrum grave est

A very literal arrangement would be:

• To the farmer an old yoke is, but a new strap to buy he wants, because the plough heavy is

That sounds strange in English, but it is normal Latin structure.

No. These adjectives belong to different patterns.

• novus, nova, novum = first-and-second-declension adjective
• gravis, grave = third-declension adjective
• vetus, veteris = also a third-declension adjective, but with its own pattern

So although all three are adjectives, they do not form their endings in the same way.

That is why the sentence has:

• vetus iugum
• novum lorum
• aratrum grave

A big part of learning Latin is getting used to these different adjective types.