Med den lange lineal kan jeg tegne en lige streg på tavlen.

This part means with the long ruler, and it has been moved to the front for emphasis.

In Danish, just like in English, you can often move a phrase like this to the beginning:

• Jeg kan tegne en lige streg på tavlen med den lange lineal.
• Med den lange lineal kan jeg tegne en lige streg på tavlen.

Both are grammatical, but the version with Med den lange lineal first gives a little more focus to the tool being used.

Also, when something other than the subject comes first in a Danish main clause, the verb usually comes before the subject. That is why you get:

• Med den lange lineal kan jeg ... not
• Med den lange lineal jeg kan ...

This is a very important Danish word-order pattern.

This is because Danish is a V2 language in main clauses. That means the finite verb normally comes in the second position.

Here, the first position is taken by:

• Med den lange lineal

So the verb must come next:

• kan

And only then comes the subject:

• jeg

So the structure is:

• Med den lange lineal = first element
• kan = finite verb in second position
• jeg = subject

Compare:

• Jeg kan tegne en lige streg på tavlen.
• På tavlen kan jeg tegne en lige streg.
• Med den lange lineal kan jeg tegne en lige streg.

This inversion is very common in Danish.

Because when an adjective comes before a noun in a definite phrase, Danish normally uses the weak form of the adjective, which usually ends in -e.

So:

• en lang lineal = a long ruler
• den lange lineal = the long ruler

Here:

• lineal is a common-gender noun
• the phrase is definite because of den
• therefore the adjective becomes lange

This pattern is very common:

• en stor bog → den store bog
• en ny stol → den nye stol
• en lang lineal → den lange lineal

Danish has two common ways of making nouns definite:

1. Suffix definite article on the noun:

   • linealen = the ruler
   • tavlen = the blackboard

2. Separate article + adjective + noun when there is an adjective:

   • den lange lineal = the long ruler

So if there is no adjective, you usually get:

• linealen

But if there is an adjective before the noun, Danish usually uses:

• den lange lineal

This is a key pattern:

• bogen = the book
• den store bog = the big book

Here lige means straight.

So:

• en streg = a line / stroke
• en lige streg = a straight line

The adjective is lige, not lig, because lig usually means something like equal or similar, while lige can mean several things depending on context, including straight.

In this sentence, lige describes the shape of the line, so it means straight.

Examples:

• en lige vej = a straight road
• en lige streg = a straight line

Because streg is a common-gender noun in Danish, so it takes en.

Danish nouns are mainly divided into two genders:

• common gender → en
• neuter → et

So you have:

• en streg
• en lineal
• en tavle

You simply have to learn the gender with the noun. A good habit is to memorize nouns together with their article:

• en streg
• en lineal
• en tavle

På tavlen means on the blackboard or on the board.

Here, the noun is definite by using the ending -en:

• en tavle = a board / blackboard
• tavlen = the board / blackboard

So på tavlen is the normal way to say on the board when you are referring to a specific board already understood from context.

You would use på den tavle if you wanted to say on that board or if you were contrasting it with another one:

• på tavlen = on the board
• på den tavle = on that board

Both can often be translated as line, but they are not always used in the same way.

Streg often means:

• a drawn line
• a stroke
• a mark

Linje often means:

• a line in a more abstract or structural sense
• a row, route, policy, or line of text

In this sentence, streg is the natural choice because we are talking about drawing a physical line with a ruler.

So:

• tegne en streg = draw a line
• en lige streg = a straight line

Because it comes after the modal verb kan.

In Danish, modal verbs such as kan, skal, vil, må are followed by the infinitive form of the main verb, usually without at.

So:

• jeg kan tegne = I can draw
• jeg vil tegne = I want to draw
• jeg skal tegne = I must draw / I have to draw

That is why the sentence has:

• kan jeg tegne

and not a conjugated form like tegner.

Yes. That is also grammatical.

This version has a more neutral word order:

• Jeg kan tegne en lige streg på tavlen med den lange lineal.

The original sentence:

• Med den lange lineal kan jeg tegne en lige streg på tavlen.

puts more emphasis on with the long ruler.

So the difference is mainly one of focus and style, not basic meaning.

Here med means with, in the sense of using something as a tool.

So:

• med den lange lineal = with the long ruler / using the long ruler

This is the normal preposition for instruments or tools:

• skrive med en blyant = write with a pencil
• klippe med en saks = cut with scissors
• tegne med en lineal = draw with a ruler

In this sentence, yes: lineal means a measuring ruler, the kind you use for drawing straight lines.

So:

• en lineal = a ruler

A learner should just note that the word looks a bit different from English, and Danish uses lineal where English normally says ruler.

A careful approximate pronunciation is:

Med den lange lineal kan jeg tegne en lige streg på tavlen

Approximate English-style guide: mel den LANG-uh lee-neh-AHL kan yai TINE-uh en LEE-uh strei pɔ TAV-len

A few useful notes:

• jeg is often pronounced something like yai in careful speech, though in fast speech it can be more reduced.
• tegne is often roughly tine-uh or tain-uh, depending on accent and speed.
• lige here sounds like LEE-uh.
• streg has a Danish vowel sound that is not exactly like English.
• tavlen is roughly TAV-len.

If you are learning pronunciation, it is best to listen to native audio, because Danish spelling and pronunciation often differ a lot.