Answer:
y < 4x - 2
Step-by-step explanation:
The shaded region is bounded by dotted line that's why the inequality must be with sign < or >.
This line passes through the points (0,-2) and (1,2). The slope of this line is
[tex]\dfrac{2-(-2)}{1-0}=\dfrac{4}{1}=4[/tex]
and the equation of the line is
[tex]y=4x-2[/tex]
becaue y-intercept is -2.
To determine wihich sign you shoul use, substitute the coordinates of the origin:
[tex]4\cdot 0-2=-2<0[/tex]
so the origin belongs to the region [tex]4x-2<y[/tex]
From the diagram you can see that origin does not belong to the shaded region, so correct inequality is
[tex]4x-2>y\ \text{or}\ y<4x-2[/tex]
