Question

Which of the following inequalities is graphed on the coordinates plane ?

Answer 1

It Should Be A

Explanation:

Answer 2

option D.

`y \geqslant 2x + 2`

Explanation:

we have two points on the line

• (0, 2)
• (-1, 0)

using these points to find the equation of the line (shown as red in the figure)

`y - y_(1) = (y _(2) - y _(1) )/(x _(2) - x _(1)) (x - x_(1))`

let,

• x₁ = -1 , y₁ = 0
• x₂ = 0 , y₂ = 2

`y - 0 = (2 - 0)/( 0 + 1) (x + 1) \\ y = 2(x + 1) \\ y = 2x + 2`

so the equation of the required line (boundary line) is y = 2x+ 2

the shaded portion is represented by inequality :-

`y \geqslant 2x + 2`

so, option D is the answer