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The phrase "a fixed line" is correct and usable in written English.
It can be used in contexts where you are referring to a line that is unchanging or established, such as in mathematics, telecommunications, or even in a metaphorical sense.
Example: "In our discussion about the project, we need to establish a fixed line of communication to ensure everyone is on the same page."
Alternatives: "a set line" or "an established line".
Exact(20)
The collection was generated by a fixed line moving through space parallel to itself.
In the United States, there is no way to distinguish between a mobile phone number and a fixed line number.
Typically a machine will cost more than £50 a month to rent, needs to be connected to a fixed line and will deduct about 1.5% of all payments.
On one occasion Jowell's unique voicemail number was called by someone using a fixed line at News International, the prosecution said.
It cost 2p a minute to phone a fixed line anywhere in the world or 14p a minute to UK mobiles (after paying a monthly fee of £7.99).
Before then, getting a fixed line meant waiting for years or renting one on the grey market for a small fortune.
Similar(39)
The average Rwandan makes about $220 a year, and a fixed-line Internet hookup costs about $90 a month.
Today, more than 90% of households have a fixed-line phone, three times the world average.
This will provide a latency similar to that offered by a fixed-line connection.
Nearly one in three Finnish households is now without a fixed-line phone.
Almost a quarter of all American households no longer have a fixed-line phone.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com