What is the nature of the current voltage graph for an unknown resistor?

Fixed-value resistors are normally manufactured so that they obey Ohm's Law -that is, the ratio of their voltage to current remains constant for variations in voltage, within specified limits. In other Words, their resistance value remains constant for variations in voltage. This would produce a straight-line curve when plotted. Devices and materials that do not obey Ohm's Law (e.g. semiconductors, etc.) would produce a curved line.