Accurate day-ahead electricity price forecasting is essential for residential welfare, yet current methods often fall short in forecast accuracy. We observe that commonly used time series models struggle to utilize the prior correlation between price and demand-supply, which, we found, can contribute a lot to a reliable electricity price forecaster. Leveraging this prior, we propose a simple piecewise linear model that significantly enhances forecast accuracy by directly deriving prices from readily forecastable demand-supply values. Experiments in the day-ahead electricity markets of Shanxi province and ISO New England reveal that such forecasts could potentially save residents millions of dollars a year compared to existing methods. Our findings underscore the value of suitably integrating time series modeling with economic prior for enhanced electricity price forecasting accuracy.Comment: 13 pages