The answer to 'how to unclog supply line' is to first try using a plunger to dislodge the clog. Plunge the drain firmly up and down several times to create suction and push the clog through. If that doesn't work, you can try using a drain snake or auger to physically break up the clog and pull it out.
Be sure to wear gloves and eye protection when working on plumbing, and avoid using chemical drain cleaners which can be harsh on pipes. If the clog persists or you're not comfortable tackling it yourself, it's best to call a professional plumber who can properly diagnose and fix the issue.