AC load line of a BJT
I will try to explain this concept but in a quite different manner than the conventional formal explanation. I hope it will be also useful for you.
The idea of this graphical representation is to reduce the circuit to two 2-terminal elements - a real voltage source with some internal resistance and varying load (the collector-emitter part of the transistor). They are connected to each other (both in series and parallel) so the same voltage is across them and the same current flows through them. Each of them is represented by its IV curve. The intersection (operating) point gives the circuit solution (the voltage and current).
The IV curve of the real voltage source is what is named &quot;load line&quot;. When the transistor changes its collector current, the moving intersection point pictures the &quot;load line&quot;. Its slope is determined by the equivalent internal resistance. In DC mode, it is only Rc; in AC mode, it is Rc||RL.
To imagine the latter, think of the coupling capacitors as of a short connection; then, Rc and RL form a voltage divider. Its output (Thevenin) resistance is Rc||RL.