Drawing the barrel adjuster away from the stud (CCW) will tighten the slack. Turning the adjuster backing to the adjuster will decrease tension. Try an simple test. Feel the cable tension, then with one hand grab the housing at the end cap and pull back, as it turning the barrel adjuster out. Notice the wire tension will increase.
The barrel adjuster of both gearing and brakes is limited. You will need to sometimes loosen the pinch bolt of the wire and draw out slack ther.