What is the slope of the line determined by

Note  that  when  x = -4  and y = 4   the equation will be  true

And when x = 4  and y = -4  the equation will also be true

So.....the points  ( -4,4)  and ( 4,-4) will be  on the graph

The  slope is  [ -4-4 ] / [4 - -4 ]  = -8 / 8  =   -1

Algebraically....we can see that

x/4  + y/4  =  0

[4x + 4y] / [xy] = 0     multiply through by xy

4x + 4y  = 0     divide through by 4

x + y =  0   rearrange as

y =  -x

So...this confirms that the slope is -1