The answer to 'why is my supply line rusty water' is that the supply line has likely developed rust inside, causing discolored or rusty water to come out. This is a common issue with older metal supply lines and can be caused by corrosion, mineral buildup, or sediment in the water. Rusty water from the supply line may indicate that the line needs to be replaced.
If the rusty water is only coming from one fixture, the issue may be isolated to that supply line. However, if the problem is throughout your home, it could be a sign of a larger issue with your main water supply line or water heater. In either case, it's best to have a professional plumber inspect the problem and provide recommendations for repair or replacement.