If you're reading your file line by line, i.e. if $line only ever contains one line, then a regular expression can't help you. The easiest way to see the second line of the file is to read two lines and discard the first, e.g. by saying

<$FILE>;
my $line = <$FILE>;
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But there's probably a reason you want to use a regular expression instead of doing this, so - what are your constraints, and what are you trying to do?