Question

why are graphs of I vs V usually drawn instead of V vs I since R= V/I
and is the gradient of I vs V = 1/R?

Answer 1

I guess (this is a guess, not a fact from a factbook :-) that the thing you can vary is usually on the vertical axis. A voltage source is a more natural device than a current source (a constant current source can be constructed with some power electronics, but you can easily construct a voltage source: a battery, a transformer, mains outlet...), and therefore it is natural to scetch the characteristic curve as the function of the voltage, not current.

This is like that you have time variable (t) usually on the vertical axis, because it is natural to think that time passes and something happens :-).