Theorem weak Hilbert

Question

If $ I $ is a proper ideal of $ K [x_1, \ldots, x_n] = F $ then $ V (I) \neq \emptyset$. dm: I want to use that $ J = \langle x_1-a_1, \ldots, a_n x_n \rangle $ is a maximal ideal of $ F $. If I prove that $ J \subseteq I$ then you would have $ I = J $ for $ J \subset I \subset F$ then $ I = J $ or $ I = F $ but the second case is given as $ I $ is proper. Then $ V (I) = \{(a_1, \ldots, a_n) \} \neq \emptyset$. I hope a suggestion that $ J \subset I$.