Yes, the values you give are correct but the graph has to include non integers, rational and irrational numbers as well.
The graph of the equation, y= x+1, is a straight line. On that line, when x= 0, y= 1 and when y= 0, x= -1. The graph of y= x+1 is the straight line through (0, 1) and (-1, 0).
The reason you should graph that line first is that it forms the boundary of the points that satisfy y< x+ 1. Obviously that line divides all of into two subsets. The points that satisfy y< x+ 1 is one of the two subsets on either side of the line. Choose a point on each side of the line to determine which side satifies the inequality.
Also, because this is y< x+ 1, rather than , you don't want to include the line itself in the graph. One way to indicate that is to use a dashed line rather than a full line.