Parallel Coordinates Plots (PCPs) are a well-known visualization technique for exploring multi-attribute datasets. In many situations, data consumers find them to be an intuitive method to analyze and interact with data. Unfortunately, using PCPs becomes challenging as the number of data items grows large or trends within data cause overlap in the visualization. The resulting overdraw can obscure important data features. A number of modifications have been proposed to PCPs, including using color, opacity, smooth curves, frequency, density, and animation, to mitigate this problem, better revealing relationships. However, these modified PCPs tend to have their own limitations in the kinds of relationships they emphasize. We propose a new interactive design for representing and exploring data relationships in PCPs. In this approach, we exploit the point/line duality property of PCPs and a local linear assumption of data to extract and to represent relationship summarizations. This approach simultaneously shows relationships in the data, and the consistency of those relationships. Our approach supports various visualization tasks including cluster analysis, mixed linear and nonlinear relationship identification, hidden pattern detection and outlier detection, all in large data. We demonstrate the results on multiple synthetic and real-world large data sets. Finally, we compare and evaluate our method with the conventional PCPs through the different visualization tasks.