Load-line of MOSFET when analyzing triode mode
The load line in your graph shows what current flows (Id) over a varying Vgs.

Your text describing triode mode and saturation concerns the behavior of Id over varying Vds (not Vgs) while keeping Vgs constant. 

Here the load line crosses the horizontal (well almost) part of the blue curves, that is the saturation region.

The triode mode region is the part on the left where the blue lines are nearly vertical.