I need help with the following problem: Sketch the set of points in the $x-y$ plane $$\{(x,x+y): x\in\Bbb R,\ y\in\Bbb Z\}.$$
What would be the best way to approach this type of problem? I tried picking some numbers and putting those points into the plane but that doesn't seem wise. These are for instance some of the points: $(0,0), (0,1), (1,0), (2,-2), (\pi, \pi)...$
If you plot this , you should get a set of horizontal parallel lines . To be exact , you will get the lines ... y=-2x , y=-x , y=0 , y=x ,y=2x ... and so on. To get an idea about this problem let x be a real number and y be a natural number. Then you will get a set of verticle parallel lines.