Question

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

Answer 1

Answer:

The correct option is 2.

Step-by-step 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

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

The related equation is

$y-(-2)=\frac{0-(-2)}{1-0}(x-0)$

$y+2=2x$

$y=2x-2$

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.

Answer 2

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.