I have a problem on the assignment and I've got stuck at one point. 

Let $\Bbb{R}$ be the group of real numbers under addition, and let $x\Bbb{Z} ⊂ \Bbb{R}$ be the subgroup which consists of all integral multiples of a given real number $x$, i.e., $x\Bbb{Z} = \{mx | m ∈ Z\}$. Prove that for any non-zero real numbers $x$, $y$, the quotient groups $\Bbb{R}/x\Bbb{Z}$ and $\Bbb{R}/y\Bbb{Z}$ are isomorphic.

First I noticed that subgroups $x\Bbb{Z}$, $y\Bbb{Z}$ form cosets of $\Bbb{R}$ which implies that they are normal subgroups. Then I know that if I can find a isomorphism (bijection) $\phi: x\Bbb{Z} \to y\Bbb{Z}$ then the quotient groups are isomorphic too. The problem is that I cannot find such a bijection.