In recent years, applications ranging from underwater navigation and construction to environmental monitoring and marine resource management have driven an escalating need for accurate and comprehensive bathymetric mapping of the marine environment. However, the complexity of the marine environment requires sound mathematical modeling of survey lines to ensure comprehensive coverage, optimal resource utilization, and high-quality data collection. This work outlines a mathematical model based on geometric and projection relationships in three-dimensional space to simulate a scenario in a designated sea area for bathymetric surveying. By knowing the slope angle of the seabed, assuming a planar seabed and considering the ship's position along a survey line, a model is developed to determine the coverage width of multibeam sonar beams on the seabed. The model involves calculating the water depth at different points along the survey line using the tangent of the slope angle, and then employing trigonometric functions and equations to establish a relationship for the coverage width, which is equal to the length of the segment intersected by the sonar beams on the seabed line. Further, the model accounts for the overlap ratio between adjacent survey stripes to optimize survey line planning for complete area coverage while minimizing resources and time. Additionally, a visualization of the seabed depth variation is suggested through plotting, simplifying the calculation by projecting the varying slope onto a horizontal plane. This approach facilitates the design of survey lines across the sea area, ensuring efficient and comprehensive bathymetric mapping.