Tropical and subtropical regions with hilly terrains experience significant precipitation. The surge in population and development in these areas has led to construction on slopes. Designing foundations on sloping terrain differs from flat regions, and the lack of guidelines and criteria for hilly areas poses challenges. Existing foundation design theories tend to overestimate soil-bearing capacity on slopes; thus, analyzing foundations on slopes should consider both bearing capacity and slope stability. Foundation design should be based on the minimum bearing capacity from both criteria. The primary approaches for evaluating the bearing capacity of shallow foundations on slopes are based on earlier established methods. The assumption of an initial failure surface and refining it often results in laborious and suboptimal solutions, a common issue with limit-equilibrium and limit analysis approaches. The slip-line method was employed, enabling the derivation of fundamental differential equations and determining slip-line networks, which depict potential slip surfaces. A MATLAB code was developed to solve these equations using the finite difference method, assessing bearing capacity. The critical slip line can be directly obtained within the plastic zone beneath the shallow foundation. A parametric study considered various setback distances, slope angles, and internal friction, validating the MATLAB code against available literature. The study examined both completely dried and fully saturated soil conditions. This research highlights the need for integrating slope stability and bearing capacity assessments to ensure the safe design of foundations on sloping terrains, addressing the challenges in hilly regions.