Why does each ordered pair (x,y) that satisfies ax + by = c correspond to a point on the graph of that equation?

Because an ordered pair represents only the x-intercept and y-intercept simultaneously, and these intercepts alone define the entire graph of a linear equation without checking the substitution

Because any ordered pair can be connected to every other ordered pair to form a polygon, which visually approximates the algebraic behavior of the equation, and thus each pair marks a vertex of that polygon

Because the ordered pair gives you a slope value directly, which then uniquely determines the location of the single point that represents all solutions of the equation

Because substituting x and y into the equation yields a true statement, and the coordinate (x,y) is the location of that true solution on the Cartesian plane, where all such true substitutions lie