B737-900
Air Traffic Control Developmental
Situational Awareness; Training / Qualification
ATC Issue All Types; Conflict Airborne Conflict; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued New Clearance; Air Traffic Control Issued Advisory / Alert; Flight Crew Took Evasive Action; Flight Crew FLC complied w / Automation / Advisory
Procedure; Human Factors; Airspace Structure
I was working a few planes in my sector and had a Cessna transitioning north at 5;500 ft. enroute VFR; which is a pretty normal operation. I released a B739 which was a factor in me analyzing whether or not I would have to expedite [the B739]'s climb to get above the VFR. When [the B739] checked in they were still within the lateral confines of Tower's airspace climbing out of 3;000 ft. approximately which made me judge that they would climb well above the VFR aircraft. With the proximity of the VFR aircraft being just past their projected path I didn't even think it was necessary to issue traffic. I think they may have begun to level off before I exchanged traffic which caused a TCAS RA event having them descend into an area of high terrain. They were really close to entering a 6;000 ft. MVA below the altitude and may have. Before entering the higher terrain I had a plain English conversation with them asking in an urgent tone if they are able to climb via except maintain 14;000 ft. because the traffic was 3 miles behind them. I'm not 100% sure if they entered the MVA below the altitude but I was a little fixated on the fact that I was about a second away from issuing a low altitude alert; followed by advise you climb and maintain 14;000 ft. immediately contrary to them still responding to the RA.In the future I'm simply going to either expedite the climb of these departures off the airport with an instruction to Tower; or more likely just have the 5;500 ft. VFR transitions landing in the next 20-30 miles descend down to 3500 ft. If they are strictly enroute; then I'll vector the 5;500 ft. aircraft south of the departure corridor to give at least two miles of lateral separation at the same altitude.
Approach Controller reported that a traffic conflict and RA caused an aircraft to fly below the MVA.