V = V_max/1 + I/K_I [S]/K_m + [S]
1/V = K_m + [S]/V_max/1 + I/K_I[S]
1/V = K_m/V_max/1 + I/K_I[S] + [S]/V_max/1 + I/K_I [S]
1/V = K_m(1 + I/K_I)/V_max · 1/[S] + 1 + I/K_I/V_max

1. Non-competitive inhibitor yields a family of lines having a common intercept on [S] axis indirectly that K_m for the substrate is not altered by a non-competitive inhibitor but V_max decreases.
2. As K_m is unchanged, the addition of high concentration of [S] does not relieve the inhibition.