I have to either show that a transformation is either linear or not due to the additivity or the homogeneity.

The first question is:

T(x,y)=(x+1,y)

I answered:

T(x)+T(y)= mx+my

m(x+1)+my= mx+m +my

mx+my =/= mx+m+my

therefore

T(x,y)=(x+1,y) is not linear under additivity.

How would I prove or disprove that the transformation is linear under homogeneity?