For this case, we must find two points that belong to the line and thus find the slope.
We have:
[tex](x1, y1) :( 1,1)\\(x2, y2) :(0,4)[/tex]
We found the slope:
[tex]m = \frac {y2-y1} {x2-x1} = \frac {4-1} {0-1} = \frac {3} {- 1} = - 3[/tex]
It is also observed that the cut-off point with the y-axis is 4.
In this way, we discard options A and B.
We evaluate option C:
[tex]y> -3x + 4[/tex]
We substitute the point (0,0) that belongs to the shaded region and verify the inequality:
[tex]0> -3 (0) +4\\0> 4[/tex]
It is not fulfilled!
Thus, the correct option is option D.
ANswer:
Option D
