The answer to 'how to unclog supply line' is to use a plunger or snake to dislodge the clog. First, try using a plunger to create suction and force the clog down the pipe. If that doesn't work, use a plumber's snake or auger to physically break up the clog and pull it out. Be sure to wear gloves and eye protection when using these tools.
If the clog is deep in the supply line or you are unable to clear it, it's best to call a professional plumber. They have specialized equipment and expertise to safely and effectively clear tough clogs without causing further damage to your plumbing system.