
die Kurve
curve / bend
A bend or curve in a path, road, or track.
Der Autofahrer nahm die scharfe Kurve zu schnell und kam von der Straße ab.
The driver took the sharp curve too fast and went off the road.
curve
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curve / bend
A bend or curve in a path, road, or track.
Der Autofahrer nahm die scharfe Kurve zu schnell und kam von der Straße ab.
The driver took the sharp curve too fast and went off the road.

curve
A line in a graph or coordinate system that represents a variable quantity.
Die Kurve auf dem Chart zeigt einen deutlichen Anstieg der Arbeitslosigkeit.
The curve on the chart shows a clear rise in unemployment.

to pull through
To just manage a difficult situation or successfully solve a problem, often after initial difficulties.
Nach einem schlechten Start ins Semester hat er mit viel Lernen doch noch die Kurve gekriegt.
After a bad start to the semester, he pulled through in the end by studying a lot.

curve / fan section
The curved area in a stadium or arena where a team's especially dedicated fans often gather.
Die Stimmung in der Fankurve war nach dem Tor unglaublich.
The atmosphere in the fan section was incredible after the goal.
Pay attention to the prepositions and the case. Movement into a bend is expressed with 'in die Kurve' (accusative), while a location is described with 'in der Kurve' (dative).
Das Motorrad fuhr schnell in die Kurve.
The motorcycle rode quickly into the curve.
In connection with roads and paths, 'Kurve' (curve) is often combined with certain adjectives and verbs. Typical phrases are 'eine scharfe Kurve' (a sharp curve), 'eine weite Kurve' (a wide curve), or 'die Kurve nehmen' (to take the curve).
Sei vorsichtig, die nächste Kurve ist sehr eng.
Be careful, the next curve is very tight.
When 'Kurve' (curve) means a line in a graph, you often find the word in the context of data, economics, or science. Signal words are 'Anstieg' (rise), 'Abfall' (decline), 'Statistik' (statistics), or 'Diagramm' (diagram/graph).
Die Kurve der Infektionszahlen flacht langsam ab.
The curve of infection numbers is slowly flattening.
The idiom 'die Kurve kriegen' (to pull through / to manage it) is a fixed unit. The image behind it is a vehicle that almost has an accident but makes the bend at the last moment. It means to just manage a difficult situation.
Er hatte große Probleme in der Schule, aber im letzten Jahr hat er die Kurve gekriegt.
He had major problems at school, but in the final year he pulled through.
The meaning 'fan section in a stadium' is easy to recognize from the sports context. Words like 'Stadion' (stadium), 'Fans' (fans), 'Gesänge' (chants), or 'Fußball' (football/soccer) clearly point to this use.
Die Fans in der Kurve feierten ihre Mannschaft mit lauten Gesängen.
The fans in the curve celebrated their team with loud chants.
line
A Linie can simply be a visible line or a line showing a connection. A Kurve, by contrast, is a line whose path changes or bends, especially in a graph. Use „Linie“ for a straight or generally depicted connection and „Kurve“ for a changing path.

Die Kurve im Diagramm steigt nach den ersten Messungen deutlich an.
The curve in the graph rises significantly after the first measurements.
Die Linie im Diagramm verbindet die beiden Messpunkte gerade miteinander.
The line in the graph connects the two data points with a straight line.