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A resistor is not a good model for a saturated BJT.  According to your graphs it is, but those are simplified.  There isn't really a single slope for all base currents as your graph shows.  Even if you can approximate some region of interest with a fixed slope, that slope will vary quite a bit between parts and with temperature.  Of course that's true of the other parts of the graph too.

In any case, if the series load is a resistor, then you know operation is always along the red line regardless of what the transistor does.