What happens to voltage when resistance is increased?

Ohms law is V=I X R. If resistance (R) is reduced and current (I) is constant, then voltage (V) must decrease. You can see from the equation that they are proportional to one another. If, however, R is reduced and V is held constant, then I must increase (I and R are inversely proportional). The only way V can increase is if either or both I and R increase.