Agraph is shown below:
solid line joining ordered pair 0, negative 2 and 1, 3 and the region below this line is shaded
which of the following inequalities is best represented by this graph?
5x + y ≤ 2
5x + y ≥ 2
5x − y ≤ 2
5x − y ≥ 2

1.
The line joins (0, -2) and (1, 3).

thus, the slope of this line is 


Using point (0, -2) and slope m=5, the equation of the line is:

y-(-2)=5(x-0)
y+2=5x

5x-y=2

2.
Thus the candidate inequalities are 

5x-y≥2 and 5x-y≤2

3.
Pick a point P not on the line, for example P(0, -3) which is clearly below the line, which is the shaded part.

check (x,y)=(0,-3) in 5x-y≥2:

5*0-(-3)≥2

3≥2, which is true

Remark: If we had picked a point above the line, for example P(0,2), we would have

5x-y≥2:
5*0-2≥2: 
-2≥2, not true, but we would pick again this inequality, since the second point was not on the colored region.

 

5x-y≥2