A couple of small things went wrong in your 2nd example.

• slurp is spelled read_file, at least in the newest CPAN version 9999.04.
• The regex is matching against $_, not $f.
• The regex is not working in multiple ways :). {$line_no-1} evaluates to e.g. {10-1} which looks for the literal string '{10-1}'. Even if this worked, it would be looking for consecutive newlines, so consecutive empty lines. And there are more mistakes ...

The correct version should be something like this:

use File::Slurp;

my $f = read_file $filename;
my $line2 = $1
  if ($f =~ m!\A(?:.*\n){@{[$line_no-1]}}(.*)\n!m);
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... but I wouldn't recommend it.

And for the sake of completeness, here the solution spelled out with Tie::File which lots of people mentioned already.

use Tie::File;

tie my @file, 'Tie::File', $filename
  or die "Couldn't tie '$filename': $!";

my $line2 = $file[9];
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