This looks like an application of the First Isomorphism theorem. I asked one of my classmates how she would go on on doing this and she said that Iwould want to define a homomorphism f: ℝ^{2}-> ℝ where f(ℝ^{2}) = ℝ and ker(f)=N.She also said that given my definition for N, she would suggest using f(x,y)=3x-4y as my homomorphism.

I am having trouble following her advice. Can anyone further explain what I should do to tackle this problem? Thanks!