Question

Which innovation of the industrial revolution led to a decrease in the price of coal from manchester

Answer 1

That would be the invention of canals.
Before the canals the coal had to be transported by  horses and also transported by some rivers. This was a time consuming and expensive endeavor which if continued would not have made Manchester the center of industry. That is why the canals were important and especially the Bridgewater Canal which cut the prices of coal in half.