How does the resistance of a filament lamp change as the voltage increase?

The resistance of a filament lamp increases as the potential difference increases because the filament becomes hot. The movement of electrons (which is what causes the current) makes the atoms inside the filament vibrate faster and this makes the filament heat up. As the filament heats up, it is more difficult for the electrons to get through the filament because it's atoms are moving so much, and because resistance measures how easily a current passes, the resistance goes up.