Resistance in a circuit?

If you have a material and you are unsure whether it is ohmic or non ohmic and you collect data for potential difference across bulb and current flowing through filament and then plot it, and it seems to be linear (i.e. seems to be ohmic as it roughly follows Ohm's Law, V = IR). And then you plot the inverse of potential difference and current flowing through the filament to get a gradient of power (due to P = V I) what does this tell you? I'm sorry if I've phrased this badly.. but does it matter if power is a constant or changing? If so, what does it mean if its constant and what does it mean if its changing?