Question

Determine whether the origin is included in the shaded region and whether the shaded region is above or below the line for the graph of the following inequality:

y > 1/2x + 2

a)The origin is not included in the shaded region, and the shaded area is above the line.

b)The origin is not included in the shaded region, and the shaded area is below the line.

c)The origin is included in the shaded region, and the shaded area is above the line.

d)The origin is included in the shaded region, and the shaded area is below the line.

Answer 1

the origin (0,0) is not in the shaded region and the shaded region is above the line because of the (>) greater then sign

Answer 2

The origin is not included in the shaded region, and the shaded area is above the line.

Explanation:

We need to find the shaded region for the given inequality

y > 1/2x +2

To determine whether the origin is included in the shaded region, we use origin (0,0)

Plug in x=0 and y=0 in the given inequality

0> 1/2(0) +2

0 > 2 that is false

So (0,0) origin is not included in the shaded region

In the inequality we have greater than symbol

for > symbol we shade above the line

The origin is not included in the shaded region, and the shaded area is above the line.