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 > one half x + 2 (5 points)


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

Answer 1

The line y = (1/2)x + 2 has a slope of 1/2 and a y-intercept of 2. Since the actual inequality is that y > (1/2)x + 2, then the shaded portion that satisfies this inequality will be above the line. Its y-intercept at (0, 2) means that the origin is below this line, so the origin is NOT included in the shaded region, and the shaded region is above the line. (This is the 1st choice).