The current through the resistor is proportional to the voltage across it. A graph with Voltage (V) plotted against curent I is a straight line.
The voltage V is proportional to the current I. At once ...
The ratio V/I is defined as R, the resistance in Ohm's (W). The resistance R is constant for metals at constant temperature.
The resistance for the red line is ...
The resistance for the blue line is ...
Ohm's law is a simple relationship in modern terms but Ohm had a difficult task. He had to make his own power supply and his own current meter. He didn't have a volt meter - he investigated the law with a constant voltage - but he probably never had a clear idea of exactly what voltage was.