die Achse
axle
A rod or shaft in technology around which wheels turn, or that connects wheels to each other.
Nach dem Unfall war die vordere Achse des Wagens gebrochen.
After the accident, the car's front axle was broken.

axis / axle
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axle
A rod or shaft in technology around which wheels turn, or that connects wheels to each other.
Nach dem Unfall war die vordere Achse des Wagens gebrochen.
After the accident, the car's front axle was broken.

You can recognize the meaning of 'Achse' (axis/axle) from the context. In technical contexts (car, bicycle), it means the shaft for wheels. In geometry or physics, it is a reference line. In politics, it describes an alliance.
Die hintere Achse des LKW muss repariert werden.
The truck's rear axle needs to be repaired.
The colloquial expression 'auf Achse sein' means that someone is on the road a lot or traveling.
Als Vertreter ist er die ganze Woche auf Achse.
As a sales representative, he is on the road all week.
In technical contexts, 'Achse' (axle) is often combined with adjectives like 'vordere' (front), 'hintere' (rear), or 'gebrochene' (broken). People also speak of the 'Achse eines Wagens' (axle of a car) or 'eines Anhängers' (of a trailer).
Bei dem alten Fahrrad ist die vordere Achse verbogen.
The front axle on the old bicycle is bent.
The phrase 'sich um die eigene Achse drehen' is a very common expression and means that something or someone turns in a circle.
Die Tänzerin konnte sich zehnmal schnell um die eigene Achse drehen.
The dancer was able to spin around her own axis ten times quickly.
In political contexts, people often speak of a 'politische Achse' (political axis) or an 'Achse zwischen' (axis between) two cities or countries. Common verbs are 'bilden' (to form) or 'stärken' (to strengthen).
Die beiden Länder wollen eine wirtschaftliche Achse bilden.
The two countries want to form an economic axis.
line
'die Linie' and 'die Achse' can both mean a straight line or look like a straight line. 'Linie' is the more general word for a visible mark on a surface. 'Achse' is used more in mathematics, physics, or technology when an imaginary reference line is important, for example in symmetry or in a coordinate system. Learners may confuse the words because an axis is often drawn as a line. Still, not every 'Linie' is an 'Achse': an 'Achse' has a specific function.

Im Diagramm zeigt die waagerechte Achse die Monate.
In the diagram, the horizontal axis shows the months.
Nach dem Unterricht markiert Jan die falsche Linie im Heft noch einmal.
After class, Jan marks the wrong line in his notebook again.