Theorem about flat module and ideal over a commutative ring

Question

Let $I$ be a right ideal of $R$ (a commutative ring) then $M$ is flat if and only if $$0\to I\otimes_R M\to R \otimes_R M \cong M$$ is exact.

($\Rightarrow$) If $M$ is flat and $i:I \to R$ is canonical injection, then we have $I\otimes_R M\xrightarrow{i\otimes 1} R\otimes_R M$ is an injection and following $R \otimes_R M \cong M$, we have the proof.

How can I proof ($\Leftarrow$), thankyou so much.