You are told of a shouting match between two employees, one a line worker - the other a supervisor from another department. How do you resolve?

I assume by 'line worker' you meant that the employee reports to you. If yes, the only immediate control you have is on your line worker. If the shouting match is relevant to the actual job/task of your line worker then you ought to listen to your line worker (i.e if it effects the way of working, i.e. safety). With regards to supervisor from other department, i guess, if you are supervising your own department, a friendly chat in a corner can resolve most issues. However it needs to made clear that your are the supervisor or the said line worker and any issues/suggestions/complaints of your line workers should come through to yourself and not directly to the line worker.