Let's solve for y
xy + y = 2x
(x+1)y = 2x
y(x+1) = 2x
y = 2x/(x+1)
As you can see, there is an x in the numerator and in the denominator. There is no way to get the equation into y = mx+c form, so the equation is not linear.
Instead, this graphs out a curved hyperbola as the diagram shows below.
This hyperbola has a vertical asymptote at x = -1 and a horizontal asymptote at y = 2
