In this paper, the graphical method for solving linear programming is extended in fuzzy environment. Here, we dealt with the fully fuzzy linear programming (FFLP) which involves fuzzy constraints and fuzzy objective. Determining and visualizing the fuzzy feasible space in the geometrical space is one of the novel contributions of this study. Defining fuzzy constraints as fuzzy lines and finding the nature of the point of intersection between fuzzy lines are also studied. The fuzzy constraints divide the geometrical into fuzzy half planes. Intersection of such fuzzy half planes yields a fuzzy convex hull. The optimal solution of fuzzy linear programming problem is obtained at an extreme point of this fuzzy convex hull. The results obtained from the proposed method are compared with existing methodologies.