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 halfx + 2 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

Answer:

The correct option is A) The origin is not included in the shaded region and the shaded area is above the line.

Step-by-step explanation:

Consider the provided inequality.

$y>\frac{1}{2}(x)+2$

The above inequality can be written as:

$y>\frac{x}{2}+2$

Now, Ignore the inequality sign and substitute x = 2 in $y =\frac{x}{2}+2$.

$y =\frac{2}{2}+2$

$y =1+2$

$y =3$

Thus, the coordinate is (2,3).

Substitute x = 0 in $y =\frac{x}{2}+2$.

$y =\frac{0}{2}+2$

$y =0+2$

$y =2$

Thus, the coordinate is (0,2).

Use a dashed line, if the signs of inequalities are < or > and use the solid line if the inequalities are ≤ or ≥.

The sign of the inequality is ">". So, draw a dashed line passing through the points (2,3) and (0,2).

Shade the area above the line if y has a greater than (> or ≥) and shade the area down if y is less than (< or ≤).

Now consider the provided inequality the sign of the inequality is ">". So shade the area above the line.

The graph is shown in figure 1.

By observing the graph it can be concluded that origin is not included in the shaded region and the shaded region is above the line.

Hence, the correct option is A) The origin is not included in the shaded region and the shaded area is above the line.

Answer 2

The answer should be the third one which is "The origin is included in the shaded region and the shaded area is above the line."

Hope this helps!!