In a current vs potential difference graph, we can obtain the value of the resistance of the component. There are books that say gradient-inverse is the resistance and also books that say the value of $\frac{\text{current, I}}{\text{potential difference:V}}$, which comes from the coordinates of the graph, provides the resistance.

I tend to believe the second method (coordinates) provide the true value of resistance. The reason is because when we discuss gradient, we are talking about change wrt to another quantity. e.g. acceleration is change of velocity wrt time. Resistance is NOT change of potential difference wrt current. Resistance is the ratio of potential difference over current, according to Ohm's law.

This is frustrating because I can find official solutions to international certified examinations also saying that the gradient method is the correct one. So can someone who is very knowledgeable in this area provides the true answer? Students need to be taught the correct methods.

Update:

The two ways to calculate the resistance from an I-V graph is:

1. Take the inverse of the gradient. In the diagram ,it would be $\frac{10-1}{15-5}=\frac{9}{10} \Omega$.
2. Take the ratio of $\frac{V}{I}$ which in this case will be $\frac{10}{5} = 2 \Omega$.

These two methods yield different results, but both give the same dimension. Which one is the correct method?

![enter image description here](https://i.stack.imgur.com/SjP1G.png)