How do you graph #absx<=absy#?

So what does this actually mean? Let's first graph the lines themselves and then work on shading next:

graph{(y-x)(y+x)=0}

Now for the shading.

So if we see the X in the graph, we want to shade all but the top slice (I can't get the graphing tool to shade properly...)

To graph the inequality |x| ≤ |y|, you can first graph the equation |x| = |y|, which represents the boundary between the regions where |x| is less than or equal to |y|.

The equation |x| = |y| simplifies to two equations: x = y and x = -y. These are the lines y = x and y = -x, which intersect at the origin (0,0) and form a 45-degree angle with the x-axis.

The region where |x| ≤ |y| lies between these two lines, including the lines themselves. It forms a wedge-shaped region in the coordinate plane that opens upwards and downwards from the origin.

Therefore, to graph the inequality |x| ≤ |y|, you shade the region between the lines y = x and y = -x, including the lines themselves.