An algebraic algorithm for predicting the joint trace distribution on the cut-face of rock slope based on the orientations and the locations of joints investigated in the borehole has been developed. Joint trace prediction is manipulated by utilizing the three dimensional plane equations of both joint planes and projection face, and the extent of trace within the projection area is calculated by considering the persistence of each joint plane. Joint trace prediction method is efficiently applied for analyzing the stability and the adequacy of support design of Gimhae Naesam cut-slope, which is structurally unstable due to slumping. Structural characteristics of rock mass is investigated by performing DOM drilling and the potential rock mass sliding inside slope face is analyzed by examining the orientations of joint planes which can induce the slope failure. Also, the efficiency of anchor support design is evaluated by considering the joint trace distribution on the anchor installation area and its sliding potential.