Why does the plot of $y=x+y$ follow the y-axis?

Question

On online graphing calculators (e.g. Desmos, Mathway), $ y = x + y $ is a vertical line which follows the y-axis. Why does it look like this?

What term is $ x $ or $ y $ counted first?

Answer 1

$y=x+y$ is equivalent to $$x=0.$$ This gives you a line parallel to the y-axis at $x=0$.

Answer 2

If you simplify the equation by subtracting $y$ from both sides, you get the equation $x=0$. Thus, $y=x+y$ represents all of the points in the $(x,y)$ plane such that their $x$-coordinate is $0$. Thus, you get a straight, vertical line, going through the origin, because this equation's solutions are all points $(0,y)$ for $y$ a real number.

Answer 3

if you subtract $y$ from both sides, you get

$x = 0$

which is a vertical line with $x$-coordinate $0$, basically the $y$ axis.