Vertical blinds break far too easily. Fortunately, there's a cure for it. WonderHowTo points out that you can use a paper clip and tape to fix a broken slat.
When a vertical slat breaks, it's often just a tiny piece of plastic that snaps off at the hole in the top. The rest of the slat is fine. Why buy a new one if you can salvage the ones you have? To save the slat, just lay a paper clip over the gap, tape it down and punch a hole through the tape. Hang it up, and you're done! You can also use a toothpick if you prefer.
If paper clips and toothpicks aren't your style, check out the source link for a few other simple ways to fix vertical blinds.