i want to know if the proper way to close an App is to double click the home button and slide up. and also if leaving the app open will use more battery.

That is Force closing an app, and is not really necessary. You close an app by using the home button and it disappears from the home screen. It is in a suspended state, not running. The phone will actually use more battery if you force close apps, since they will have to load completely again when you need the app. You are better just to leave them alone. However, if you are insistent on the procedure, you double-tap the home screen and swipe upwards on the preview of the app on the screen to force close it.

See: http://www.howtogeek.com/204552/no-closing-background-apps-on-your-iphone-or-ipa d-wont-make-it-faster/