Question

the line will be drawn once all required data is provided and will update whenever a value is updated. the regions will be added once the line is drawn.

choose the type of boundary line:
solid (-)
dashed (--)

enter two points on the boundary line:
\\((-6, 0)\\) \\((0, 3)\\)

select the region you wish to be shaded:
a
b

Explanation:

Identify the boundary line type

Using the Graphing Linear Inequalities in Two Variables knowledge point
The boundary line shown on the grid is solid.
Solid (-)

Identify the two points on the boundary line

Using the Plotting Points and Intercepts of a Line knowledge points

$$
LATEXBLOCK0
$$

Determine the equation of the boundary line

Using the Intercepts of a Line knowledge point

$$
LATEXBLOCK1
$$

Determine the shaded region

Using the Graphing Linear Inequalities in Two Variables knowledge point
The image shows a line dividing the coordinate plane into two regions: region A (below the line) and region B (above the line). Since the final shaded region is not yet selected, we can describe the options:

• Region A represents the half-plane below the line \(y \le \frac{1}{2}x + 3\).
• Region B represents the half-plane above the line \(y \ge \frac{1}{2}x + 3\).

Answer:

• Type of boundary line: Solid (-)
• Two points on the boundary line: \((-6, 0)\) and \((0, 3)\)
• Region to be shaded: Select A if the inequality is of the form \(y \le \frac{1}{2}x + 3\) (shading below the line), or select B if the inequality is of the form \(y \ge \frac{1}{2}x + 3\) (shading above the line).