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:

A) The origin is not included in the shaded region and the shaded area is below the line.
B) The origin is included in the shaded region and the shaded area is above the line.
C) The origin is included in the shaded region and the shaded area is below the line.
D) The origin is not included in the shaded region and the shaded area is above the line.​

Answer 1

Answer: D

Explanation:

Answer 2

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

Explanation:

First of all, let's find the shaded region for our given inequality:

y > ⅓x +4

To determine whether the origin is included in the shaded region, let's put in the value of x and y at the origin (0,0)

Plugging in x = 0 and y = 0 into the inequality gives;

0 > ⅓(0) + 4

0 > 4

0 is not greater than 4 like it states and thus it is false

Therefore, we conclude that the point (0,0) which is the origin is not included in the shaded region

In the inequality we have the symbol ">" which means greater than. For that symbol, we usually shade above the line on the inequality graph.

The only option that corresponds to our answers is option D