So i know the definition of a convex set:

Set S is convex then tx+(1-t)y belongs to S for all 0<t<1

I have to decide whether the following set is convex:

{(x,y); x-y<=1}

I started with tx+(1-t)y = t(x-y)+y <= t+y

then I am stuck.

edit: hm I think I might have been mixing up the the points that I choose (x,y) with the variabels in x-y<=1...

I redid it with matrices and this is what i came up with:

(1 -1)(x1,x2) <= 1 , c = (1 -1)

cx <= 1

cy <= 1

=> c(tx + (1-t)y) = tcx+(1-t)cy <= t + 1 -t = 1

Is this the correct way to solve the problem?