Intermediate Algebra
Because each plotted ordered pair only approximates the true solution set, and the line between them is a convenient sketch that stands for a finite set of points but not actual infinite solutions
Because plotting discrete integer-ordered pairs proves algebraically that values only at integer x are solutions; continuous points are assumed but are not actual solutions unless proven separately
Because linear equations produce straight-line graphs: if multiple plotted points are collinear, then every point on the continuous line between and beyond them will satisfy the same equation, giving infinitely many solutions
Because a graph is only an illustration; the true solutions are only those few points calculated algebraically, and the line is just a visual aid to estimate other values approximately rather than exact solutions