Almost the first lesson of mine that was observed by another Physicist was on Electricity and I was told afterwards that my classes should be able to recite back 'V = IR' whenever anyone said 'What's Ohm's Law?'. Yet that's not really Ohm's Law at all:
An object obeys Ohm's Law if V is proportional to I
That's all there is to it. It's therefore more like Hooke's Law, in that it's a law that some objects (e.g. resistors) obey quite well and others (e.g. filament bulbs) don't. So, just as you might say that most springs obey Hooke's Law for a certain range of loads, most resistors obey Ohm's Law for a certain range of temperatures. By contrast, rubber bands don't obey Hooke's Law and bulbs don't obey Ohm's Law.
V = IR is actually just the (rearranged) definition of Resistance: R = V ÷ I. Since it's a definition, this must be true even when an object isn't obeying Ohm's Law. This brings us on to how to measure resistance values from a V-I graph.