Answer:
option D.
[tex]y \geqslant 2x + 2[/tex]
Step-by-step explanation:
we have two points on the line
using these points to find the equation of the line (shown as red in the figure)
[tex]y - y_{1} = \frac{y _{2} - y _{1} }{x _{2} - x _{1}} (x - x_{1})[/tex]
let,
- x₁ = -1 , y₁ = 0
- x₂ = 0 , y₂ = 2
[tex]y - 0 = \frac{2 - 0}{ 0 + 1} (x + 1) \\ y = 2(x + 1) \\ y = 2x + 2[/tex]
so the equation of the required line (boundary line) is y = 2x+ 2
the shaded portion is represented by inequality :-
[tex]y \geqslant 2x + 2[/tex]
so, option D is the answer
