Any point on the graph of $y = x$ will have $x$ and $y$ coordinates same. The line passes through the points $(0,0),(1,1)$ and $(-1,-1). $

Again, any point on the graph of $y=-x$ will have $x$ and $y$ coordinates of opposite signs. The line passes through the points $(1,-1)$ and $(-1,1).$

Also, $(0,0)$ satisfy $y=-x.$

The graph of linear equation $y = x$ and $y =- x$ on the same Cartesian plane is shown in the figure given below.

We observe that the graph of these equation passes through $(0,0) .$