The answer to 'why is my supply line constantly running' is that a malfunctioning toilet fill valve is the most common cause. The fill valve is responsible for refilling the toilet tank after each flush, and if it's not working properly, it can cause the water to continuously run. This can waste a significant amount of water and increase your utility bills.
Other potential causes include a leaky flapper, a problem with the toilet tank level, or issues with the plumbing connections. If the supply line is constantly running, it's important to address the issue as soon as possible to prevent water damage and high water bills.