Is it generally possible while using source code management to figure out in what version of a file a specific line was added? If so, what SCM systems support this?
It would be a poor version control system that didn't allow you to do this. A technical term for displaying the origin of lines by version is annotating a controlled file with its history. Recently, newer RCS like
git have switched to calling the action blame instead, but the functionality is the same. Searching for those two terms will tell you how to do it in your RCS of choice.
In perforce the easiest way is to run p4v and look at the file's "Time-lapse view".
For every line of code you can see which revision it was added, and if you fiddle with the range sliders at the top you can see which lines were deleted.