Question

As the electric current in a lightbulb is slowly increased, the filament glows more and more brightly. Why does this happen?

Answer 1

As current passes through the filament the electrons of filament atoms gets energy and jump from lower to high energy level, when the come back their normal energy level they releases energy in the form of light.
If the current in lightbulb increases more electrons will go to higher energy level and when they come back they release more energy.
(more electrons more energy)