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.
Accepted Solution
A:
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).