That's a typical graph of Vce vs Ic for a bunch of Ib as provided by the manufacturer. Is my understanding correct:
We create a loadline so that we can operate the transistor's collector ckt in a linear fashion for a varying base input.
Basically there are an infinite set of Vce vs Ic curves for each and every base current value possible - obviously manufacturer's can't plot all that so they give us certain typical curves.
Q represents the DC operating point for some base current but when an input signal is fed for amplification, the base current changes, and we basically move to a different Vce vs Ic curve (the new Q point on this curve represents the output for the new base current flowing as a result of changed Ib due to signal).
Because the load line is linear, for every change in Ib we get a linear change in Ic; if the load line was somehow a sinusoid we'd get a sinusoidal amplification action for Ib?