Does $\frac{V}I = k$ necessarily imply that the wire follows Ohm's Law?
https://i.sstatic.net/ClEqP.jpg
Say, for a range of about 15 Volts, I get a good $\frac{V}I = k$ result, after which the ratio does not hold good. Does this imply the $\frac{V}I =$ Resistance?
Ohm's law is not $\frac VI=R$ where a resistance $R$ is related to the voltage drop $V$ across a circuit element with current $I$. This equation just tells you the resistance of the circuit element given $V$ and $I$. Ohm's law only holds when $R$ is constant as either $V$ or $I$ varies, i.e. $V(I)=RI$ is a linear function.
You can always get a number for $V/I$ when measuring voltage and current, so that is not an indicator of Ohm's law holding for your device. Since you get different values, your device is not Ohmic
