It is inversely proportional to it. It is proportional to the inverse square of it. As galaxies move outward, they are replaced with new matter created to take its place. The farther away a galaxy is from us, the faster it is moving away, because of the big bang. Galaxies are not moving through space, it is space that is expanding over time.
Galaxies are stationary but time continues to change, giving the appearance of motion.
They are rapidly moving away from us. Their light has been gravitationally redshifted. Their light has lost energy over time while traveling this distance. In the time it took their light to reach us, the universe expanded and, thus, their wavelengths. Its density fluctuations determined the overall large-scale structure of the universe.