Question

graph the solution set of the following linear inequality:

\\3x \ge 6y - 18\\

answer 2 points

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:
( , )( , )

select the region you wish to be shaded:
a
b

Explanation:

Determine the boundary line type

Using the Graphing Linear Inequalities in Two Variables knowledge point
The inequality is \(3x \ge 6y - 18\). Since the inequality symbol is \(\ge\) (greater than or equal to), the boundary line is solid.

Find two points on the boundary line

Using the Intercepts of a Line knowledge point

$$
LATEXBLOCK0
$$

Determine the shaded region

Using the Graphing Linear Inequalities in Two Variables knowledge point

$$
LATEXBLOCK1
$$

Since the test point \((0,0)\) satisfies the inequality, the region containing \((0,0)\) is shaded. On the graph, the line passes through \((-6,0)\) and \((0,3)\). The region containing the origin \((0,0)\) lies below and to the right of this line.

Answer:

• Type of boundary line: Solid (-)
• Two points on the boundary line: \((-6, 0)\) and \((0, 3)\)
• Shaded region: The region containing the origin \((0,0)\) (below and to the right of the boundary line).