In common emitter circuits an increase in Base voltage causes a decrease in Vout and a decrease in Base voltage produces an increase in Vout. In other words the output signal is 180o out-of-phase with the input signal. The Voltage Gain of the common emitter amplifier is equal to the ratio of the change in the input voltage to the change in the amplifiers output voltage. Then ΔVL is Vout and ΔVB is Vin. But voltage gain is also equal to the ratio of the signal resistance in the Collector to the signal resistance in the Emitter or:
Vout/Vin = ΔVL/ΔVB = -(RL/RE)