blau
blue
The color that corresponds to the sky on a clear day or the deep sea.
Der Himmel ist heute strahlend blau.
The sky is bright blue today.

blue
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blue
The color that corresponds to the sky on a clear day or the deep sea.
Der Himmel ist heute strahlend blau.
The sky is bright blue today.

In English, 'blue' can also mean 'sad'. In German, 'blau' (blue) does not have this meaning. It refers either to the color or, colloquially, to someone being drunk.
Er war nach der Party ziemlich blau und fand den Weg nach Hause nicht mehr.
He was pretty drunk after the party and couldn't find his way home anymore.
The meaning 'betrunken' (drunk) for 'blau' (blue) is used only in colloquial language. In formal situations or written language, this expression is uncommon.
Sei vorsichtig, nach drei Bier ist er oft schon blau.
Be careful, after three beers he is often already drunk.
The expression 'blau machen' (to skip work/school) means not to go to work or school. The verb 'machen' (to do / to make) is conjugated, while 'blau' (blue) remains unchanged at the end of the clause.
Weil das Wetter so schön war, hat sie spontan blau gemacht.
Because the weather was so nice, she spontaneously skipped work.
In the idiom 'mit einem blauen Auge davonkommen' (to get off lightly), 'davonkommen' (to get away / to come out of it) is the conjugated separable verb. The person who has a lucky escape is the subject of the sentence.
Mein Fahrrad ist kaputt, aber ich bin mit einem blauen Auge davongekommen.
My bike is broken, but I got off lightly.
The expression 'ins Blaue' (into the blue) is often used with verbs of movement or planning, e.g. 'fahren' (to drive / travel), 'reden' (to talk), or 'planen' (to plan). It means that you do something without a fixed destination or concrete plan.
Wir haben keine genauen Urlaubspläne, wir fahren einfach ins Blaue.
We don't have any exact vacation plans; we're simply driving off into the blue.
to be absent / to be missing
'fehlen' and 'blau machen' can both mean that someone is not at school or at work. 'fehlen' is neutral: the person is not there, and the reason may be illness, permission, or something unknown. 'blau machen' is colloquial and means that someone deliberately stays away without permission. Learners may therefore confuse the words if they only think of 'not being present'. For a neutral statement, use 'fehlen'. If you want to clearly say that someone is skipping or staying away without an excuse, 'blau machen' fits.

Tom macht blau und geht statt zur Arbeit an den See.
Tom skips work and goes to the lake instead.
Heute fehlen drei Schüler, weil sie krank sind.
Today three students are absent because they are sick.