  We present a formula for the number of line segments connecting q+1 points of
an n_1 x...x n_k rectangular grid. As corollaries, we obtain formulas for the
number of lines through at least q points and, respectively, through exactly q
points of the grid. The well-known case k=2 is so generalized. We also present
recursive formulas for these numbers assuming k=2, n_1=n_2. The well-known case
q=2 is so generalized.
