The current in the series circuit is equal everywhere, so the voltage change across the fixed resistor is only related to the current flowing through this (fixed size resistor). U=I*R, r is a constant, and u is proportional to i. The voltage across the sliding rheostat can be obtained by subtraction. (The total voltage is constant, and the voltage change at both ends of the fixed resistor is obtained from the previous)
In parallel circuit, the voltage is constant and the current changes (will the total current increase or decrease? Is the resistance of the power supply considered? Is the voltage across the power supply resistor increasing or decreasing, and should the terminal voltage of the parallel circuit remain unchanged? For a fixed resistor, the change of voltage is the change of current, and the terminal voltage of sliding rheostat is done by subtraction.