For this case, we chose two points through which the line passes and we find the slope of it, knowing that the cut point with the y axis is 2.
[tex]m = \frac {y2-y1} {x2-x1}[/tex]
The chosen points are:
(0.2)
(-4.0)
[tex]m = \frac {0-2} {- 4-0}\\m = \frac {-2} {- 4}\\m = \frac {1} {2}[/tex]
The line is given by:
[tex]y = \frac {1} {2} x + 2[/tex]
We evaluate a point of the shaded region in each one of the options to know which one is fulfilled.
We choose the point (x, y) = (2,1)
Option A:
[tex]y \leq \frac {1} {2} x + 2\\1 \leq \frac {1} {2} (2) +2\\1 \leq 3[/tex]
If it is fulfilled.
Option B:
[tex]y\geq \frac {1} {2} x + 2\\1\geq \frac {1} {2} (2) +2\\1\geq 3[/tex]
It is not fulfilled
Answer:
Option A
