This paper presents the study of momentum and heat transfer characteristics in a hydromagnetic flow of dusty fluid over an inclined stretching sheet with non-uniform heat source/sink, where the flow is generated due to a linear stretching of the sheet. Using a similarity transformation, the governing equations of the problem are reduced to a coupled third-order nonlinear ordinary differential equations and are solved numerically by Runge-Kutta-Fehlberg fourth-fifth-order method using symbolic software Maple. Our numerical solutions are shown to agree with the available results in the literature and then employ the numerical results to bring out the effects of the fluid-particle interaction parameter, local Grashof number, angle of inclination, heat source/sink parameter, Chandrasekhar number, and the Prandtl number on the flow and heat transfer characteristics. The results have possible technological applications in liquid-based systems involving stretchable materials.