Question

graph the solution set of the following linear inequality:

\\-3y \le -3x + 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 Solving Linear Inequalities knowledge point
The inequality is given as:

$$ -3y \le -3x + 18 $$

Since the inequality symbol is \(\le\) (less than or equal to), the boundary line is included in the solution set. Therefore, the boundary line must be solid.

Solve for the boundary line equation

Using the Solving Linear Inequalities knowledge point

$$
LATEXBLOCK0
$$

Find two points on the boundary line

Using the Intercepts of a Line and Graphing Linear Equations knowledge points

$$
LATEXBLOCK1
$$

Determine the shaded region

Using the Solving Linear Inequalities knowledge point

$$
LATEXBLOCK2
$$

Since the test point \((0,0)\) satisfies the inequality, the region containing \((0,0)\) (which is above and to the left of the line \(y = x - 6\)) is shaded.

Identify the region label

The boundary line \(y = x - 6\) passes through \((0, -6)\) and \((6, 0)\). The region containing \((0,0)\) lies above this line. In standard graphing interfaces of this type, Region A typically represents the upper/left region and Region B represents the lower/right region relative to the boundary line. Since \((0,0)\) is above the line, the shaded region is Region A.

Answer:

• Type of boundary line: Solid (-)
• Two points on the boundary line: \((0, -6)\) and \((6, 0)\)
• Region to be shaded: Region A