$Hom_R(R,R/I)$ isomorphic to R/I as R-modules

Question

If R is a ring and $I \subset R$ is an ideal. How can we show that $Hom_R(R,R/I)$ isomorphic to R/I as R-modules?

Do we need to choose an f in our $Hom_R(R,R/I)$ and show that we have a bijective mapping to a g in R/I?

Any help would be appreciated. Thank you.

Answer 1

I suppose that $R$ is commutative with a unit, define $H:Hom_R(R,R/I)\rightarrow R/I$ by $H(f)=f(1)$.