SOLUTION: The graph is as follows: x axis left to right is -4 ,-2, 0, 2, 4 y axis bottom to top is the same as the x axis. There is an angular line from -4 x axis to -4 y axis The quest

The graph is as follows:
x axis left to right is -4 ,-2, 0, 2, 4 
y axis bottom to top is the same as the x axis.
There is an angular line from -4 x axis to -4 y axis
The question reads: The graph represents which inequality?

You are given the graph of this line:



First we have to determine what EQUATION this line 
represents. Then we'll decide from that what 
INEQUALITY is represented by the graph.

The line goes through the points (-4,0) and (0,-4)

Therefore its slope is given by the formula:

     y2 - y1
m = ---------- 
     x2 - x1

where (x1,y1) = (-4,0) and (x2,y2) = (0,-4) 

     (-4) - (0)      -4 - 0     -4
m = ------------- = -------- = ---- = -1
     (0) - (-4)       0 + 4      4 

Then we use the point-slope formula:

y - y1 = m(x - x1)

y - 0 = -1(x - (-4) )

    y = -1(x + 4)

    y = -x - 4

That's the EQUATION of the LINE only.

Now since I cannot see the drawing
in your book or assignment, I cannot
neither tell whether:

A.  the line is a dotted line or a solid line

nor whether

B. the region above the line is shaded
   or whether the region below the line is 
   shaded.

and you didn't tell us.  So I'll give you all
four possibilities:

1. If the line is DOTTED and the region ABOVE the
line is shaded, then the INEQUALITY which 
represents the shaded region ONLY is y > -x - 4

2. If the line is DOTTED and the region BELOW the
line is shaded, then the INEQUALITY which 
represents the shaded region ONLY is y < -x - 4

3. If the line is SOLID and the region ABOVE the
line is shaded, then the INEQUALITY which
 represents BOTH the shaded region AND the line
is y > -x - 4

4. If the line is SOLID and the region BELOW the
line is shaded, then the INEQUALITY which
represents BOTH the shaded region AND the line
is  y < -x - 4

Edwin