The resistance of a device is defined by  R = V / I  and not as the gradient of the V - I  graph. The two outlooks happen to give the same answer in the case of an ohmic device (one that obeys Ohm's Law and which has a straight line V - I  graph). So, if you want to discuss the way in which resistance changes under different conditions, and all you have is a V - I  graph, you will have to read off corresponding pairs of V and I  from the graph and then calculate the various resistances.

Ohmic devices (wires and resistors) : left-hand graph

The resistance is constant. If you double the voltage, then you will double the current (and vice versa), so that the ratio stays the same. Ohms Law (that pd is directly proportional to current) is obeyed.

Metal filament lamps : middle graph

Near the origin both the current and pd are small. On the other hand you don't go (relatively) so far along the pd axis as you do up the current axis; so the ratio pd/current is quite small. The resistance is low. What is more, because the power (= V ´ I) is low, the filament is quite cool. Cool wire has a low resistance.

Far from the origin both the current and pd are high. On the other hand we have gone (relatively) much further along the pd axis than we have up the current axis; so the ratio pd/current is much larger. The resistance is high. What is more, because the power (= V ´ I) is now high, the filament is quite hot (white-hot, in fact!). Hot wire has a high resistance.

Notice that a wire's resistance reacts to temperature the opposite way to that of a thermistor.

Diodes : right-hand graph

The bend in the curve occurs around V = 0.7 V.

At lower pd's than this, the current is almost zero, so the resistance is very high indeed.

At higher pd's the current rises to a relatively high value that is determined by conditions elsewhere in the circuit. The resistance is now much lower, since current occurs on the bottom line of V/I.

Resistance is not a very useful concept when discussing diodes since the value you end up ascribing to it is determined by conditions elsewhere in the circuit.