Line fitting is widely applied across various fields to model relationships between variables, often in contexts where measurement error bounds are associated with sensor accuracy. These error bounds define a feasible parameter set (FPS), represented as a convex polygon in parameter space. This study introduces the Corridor Method to efficiently and exactly describe the FPS and proposes using the polygon’s centroid as an optimal estimate when no distributional assumptions are available. In a second scenario, where errors are bounded and assumed to follow a normal distribution, a common occurrence in practice, finding the most likely line within the FPS becomes a convex quadratic optimization problem, typically solved by computationally intensive iterative methods. Here, we expand the solution by leveraging the geometry of the likelihood function, which transforms the convex quadratic optimization problem into a sequence of one-dimensional optimizations with analytical solutions along the polygon edges. This approach provides an exact and non-iterative solution. In both scenarios, extensive testing across diverse error distributions and sample sizes demonstrates that the proposed methods provide fast and accurate estimates, outperforming Ordinary Least Squares, Constrained Linear Least Squares, and the Regularized Chebyshev Center. A MATLAB implementation of the proposed method is publicly available, providing a practical tool for precise and efficient line fitting in bounded-error settings.