Is my brake line bad?
From your description the brake cable (or the rear caliper) may be rusted up.  (Although, if you "got the brakes replaced" whoever did that should have checked brake operation and lubed the cable and caliper if necessary.)  

Observe the rear caliper as you squeeze the handle -- gentle motion on the handle should result in smooth closing of the caliper, and you shouldn't feel any significant resistance in the brake lever until the caliper is closed against the rim.

Do note that there's a lot of stretch in the rear brake cable (because it's so much longer than the front), so once the caliper is closed against the rim the cable will continue to stretch as you squeeze.