I've run into this problem many times now.
Every time I want to align just one line, I can't do it without a lot of other text jumping along with it.

How can I prevent other text from also being aligned with only one line?

Paragraph alignment works on the entire paragraph - you can't pick individual lines in a paragraph to align that without impacting all the other lines in that paragraph.

So the first thing is to check that your 'line' is a entire paragraph and not just a line within a larger paragraph.

If that is the case, then you may be dealing with a style that is set to 'automatically update'. See this to learn more Whole Document Reformatted

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Andrew Lockton
Chrysalis Design, Melbourne Australia