Voltage transfer curve; MOSFET
As you change \$V_{GS}\$ the transistor's conductivity will change, meaning that \$I_{DS}\$ will change. Now, because you have added a resistor to the circuit, KVL tells us that
$$ V_{DS} = V_{SUPPLY} - R \times I_{DS}$$
So, \$V_{DS}\$ must change as you change \$V_{GS}\$, and it changes in a way that satisfies KVL and Ohm's Law.

Try drawing a straight line on your family of curves connecting all of the points that satisfy the equation above. You will see that this is the path that your transistor takes as it moves from cutoff, to saturation, to linear behavior.