explain the relationship between resistance and voltage in a filament lamp

As voltage increases across the filament, the current also increases. The increase in current causes the temperature in the filament to rise. The increase in temperature causes the resistance within the filament to increase.
For more understanding:Higher voltages indicate that electrons have more energy causing them to move faster through the wire.Current is the rate of flow of electrons through the wire so the higher voltage causes a higher current.As electrons pass through the wire, they are deflected by the metal ions. this causes the metal ions to vibrate increasing their temperature. if the electrons move faster they hit the ions harder and cause them to vibrate more causing a higher temperature.When the electrons interact with the metal ions, they lose energy; this is 'resistance'The more the metal ions vibrate, the more collisions occur with the electrons causing a higher resistance