Flight Instructor reported an NMAC event during cruise with a descending King Air on a collision course. The Flight Instructor took evasive action to avoid a collision.

Narrative

Me and my student were transitioning from West to East of ZZZ to ZZZ1. We were cleared on the transition. While on the transition we were cruising and I noticed on my ADS-B that I was on a collision course with Aircraft Y and had gotten no traffic advisory from Tower. I noticed on my ADS-B that I got a warning on my iPad for traffic. I made the split second decision to turn northwest bound to avoid the traffic and climbed to avoid the traffic conflict; I do understand that my turn north bound increased the closer rate; while in my left turn northwest bound was I instructed to keep the heading more turn northwest bound. I put the airplane out of side on the right and maintained visual separation until it passed behind and continued East. I do believe that if I continued East it would have been much closer. I would not have made that turn if I thought we would have been cleared of conflict. As we turned North I heard the traffic advisory going off in the Tower. What I believe I should have done is be at a higher altitude. It would have also helped if I was given a traffic advisory about a plane. When transitioning stay at a higher altitude at the minimum of 2500. What I will do in the future is only transition at 2500. In the future as well if I see a possible traffic situation and I am not notified I will simply speak up and address my concerns. While flying I noticed on my iPad on final for XXL was Aircraft Y I only know this because of my iPad and ADS-B I had no visual contact with the airplane and was given no advisory about it. We continued at 2100 and I kept watching the Aircraft Y on my iPad still descending first 600 ft. above us and with 2 miles they were 200 ft. above and descending. I still had no visual contact with the airplane no was given no advisory about the plane. I couldn't see them on our left because of the right seat in the Aircraft X. So within a mile I decided to make a pilot in command decision and stay west of XXR center line and turn northwest bound so I can see the plane descending on me. As soon as I turned northwest bound I got visual on the airplane and maintained visual separation. After I passed behind I continued East. When I turned northwest bound I believe I set off the Towers traffic advisory. What could of I done different; one stay at 2500 even though I wasn't given an altitude restriction. Two told Tower that I noticed a much faster airplane on final on a collision course with us. I could have also turned right instead of left I believe I turned left because I wanted to see the airplane first.