Grafting branches

Can a branch live without its root or vine?
Have you ever seen a branch living long once it's been removed from the tree?
When I prune my trees after they have bloomed, they continue to bloom for a day or two and then it all dies.
It does not produce any fruit and after a little bit of time is just a dried up stick that isn't good for anything but starting a fire.
But, I also have a tree that grows both plums and apricots. How?
The apricots branches were grafted to the plum tree after they were removed from their root.
They were not originally a part of the plum tree, but now the plum root is what nourishes them and allows them to bear fruit.
God has grafted us into his root. He is the root and we are the branches. Without him we will eventually become a dried up stick good for nothing but the fire.
Because we were removed from our sinful root, we now bear fruit from his nurishment. Without it we die.

Belief Statement:
I believe that I am now grafted into Gods vine and will bear fruit for him.