There's a couple of problems with that string. For one, variable interpolation doesn't occur at all within single-quote delimited strings. Even if you had used double quotes as your string delimiter, however, you can't have a quoted string array index within a double-quote delimited string without using complex syntax or omitting the quotes around the index. What's more is that it's entirely possible that the index you're after isn't even a string at all but a number, in which case you shouldn't even be quoting it at all.
More information/examples on variable interpolation (including arrays) can be found on this manual page: [man]string[/man].
Also, depending upon what $line contains, don't forget about data sanitization (e.g. via [man]mysql_real_escape_string/man).