Question

Choose the linear inequality that describes the graph. The gray area represents the shaded region.

y ≤ 2x – 2

y ≥ 2x – 2

y ≥ 2x + 2

y ≥ –2x + 2

Answer 1

The given line has the equation y = 2x - 2, so if the gray area is the one of interest, the inequality is y ≥ 2x – 2.

Answer 2

The correct option is 2.

Explanation:

From the given graph it is noticed that the related line passing through the points (0,-2) and (1,0).

If a line passing through two points, then the equation of line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

The related equation is

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

`y+2=2x`

`y=2x-2`

So, the related equation is
`y=2x-2`.

From the graph it is noticed that the point (0,0) contained in the shaded region.

check the related equation by (0,0).

`(0)=2(0)-2`

`0=-2`

This statement is true if the sign is
`\geq` insted of equality.

Therefore the required inequality is

`y\geq 2x-2`

Option 2 is correct.