In the bottom picture, it looks like the broken fitting is a 1/2" FPT just like the other end (that isn't broken). If that's the case (and the old line had a couple of inches of slack in it), you should be able to purchase new fittings and reuse the old line. Looks like you'll need to cut off the broken fitting and take the rest of the hose to Home Depot or Lowe's so you can match the hose size to a nylon barbed hose to 1/2" Female Pipe Threat (FPT) fitting and an appropriately-sized hose clamp. If you can't find a barbed x 1/2" FPT fitting, a barbed x M (male)PT will work. You'll just have to add a 1/2" FPT Coupling to the end of it (either Galvanized or CPVC (cream colored - for Hot Water). First, slide the hose clamp onto the cut end of the hose, then push the barbed end of the fitting into the hose. Sometimes, a few drops of dish soap will lubricate the inside of the hose, so the fitting slides in easier. After you've inserted the barbed hose fitting into the hose, tighten the hose clamp around it, so the fitting doesn't pop out under pressure. Then reconnect the hose just like the original.
Another possible option would be to pick up a 4-5' length of PEX tubing, but it to length, and push "Shark-Bite" 1/2" PEX to 1/2" MPT fittings onto both ends. Shark-Bite fittings are a little more expensive than method #1, but they're easy to install, are water tight, and are easy to remove if needed.
Hope that helps you out. Good Luck with your project!
2013 Eagle 266RKS
2011 Ford F-150 w/3.5L Ecoboost & H.D. Tow Package