If you know the contents of the line, this is an ideal use case for:
git log -S <string> path/to/file
which shows you commits which introduce or remove an instance of that string. There’s also the -G<regex> which does the same thing with regular expressions! See man git-log and search for the -G and -S options, or pickaxe (the friendly name for these features) for more information.
The -S option is actually mentioned in the header of the git-blame manpage too, in the description section, where it gives an example using git log -S....