How does Hubble's Law relate to the Big Bang Theory?
Hubble's observations of an expanding universe lead to the Big Bang Theory.
Hubble's law shows the mathematical relationship between the distance from the earth and rate of expansion observed. The further from the earth the faster the object is moving away from the earth.
The implications of Hubble's Law are that everything in the universe was closer together, and that the Universe had a beginning.
This beginning of the universe implied by Hubble's observations and law is called the Big Bang Theory. The Theory is that the universe had a beginning starting from a central point resulting in a rapid expansion of the universe.
Before Hubble's law scientists believed that the universe was eternal and had always existed in its present state. The Big Bang Theory changed all that by showing that the universe had a beginning and was not eternal. ( Note in 1997 further observations showed that rate of expansion was increasing, which means that the universe will not only have a beginning it will also have an ending.)
Hubble's law and observations are the foundation of the Big Bang Theory.