How does Hubble's Law support the Big Bang Theory?

Actually Hubble's law was discovered before the Big Bang theory was formulated. The Big Bang Theory is an attempt to explain the observations that led to Hubble's Law.

Before the 1900s the theory was that the universe was eternal and self existent. The idea was that the universe was in a steady state having always existed and would always continue to exist. Albert Einstein even changed the equations in his general theory of relativity to reflect the idea of a steady state. Later he called putting in a fudge factor to result in a steady state the worse mistake of his life.

Hubble observed that most of the universe has a red shift indicating that the universe is expanding and moving away from itself. The further out that the universe is observed the faster it is moving apart. These observations were inconsistent with a steady state universe.

The Big Bang theory extrapolated backwards. If the universe is expanding and spreading out from itself then further back in time the universe was closer together. The Theory explained Hubble's observations by the idea that at the beginning of time ( for our universe) all the matter and energy were together in one place.

This super dense ball of matter and energy then exploded outwards creating space and time as it is presently observed. The question was would the forces of gravity and black holes bring the matter and energy back together again. The answer found in 1998 was no. The rate of the expansion of the universe is increasing not slowing down and the universe will not collapse back into the super dense ball of matter that it began as.

The Big Bang Theory postulated based on the empirical evidence that our universe had a beginning and it will eventually cease to exist. The conclusion based on Hubble's observations is that matter and energy are not eternal and self existent.

Hubble's Law provides evidence for the Big Bang Theory by showing how the universe is expanding and how galaxies are moving apart, both of which suggest a past singularity and an initial, explosive event.