https://file.aiquickdraw.com/mathbot/file/1728731053024wrdlpuq6.jpg

https://file.aiquickdraw.com/mathbot/file/1728731053025aqvay9oy.jpg

The linear inequality in your image is:

\[
-3y + 18 \leq 6x
\]

Let's solve for \( y \) to graph the inequality:

1. **Isolate \( y \)**: Start by subtracting 18 from both sides:
   \[
   -3y \leq 6x - 18
   \]

2. **Solve for \( y \)**: Divide both sides by -3 (and remember to reverse the inequality because we're dividing by a negative number):
   \[
   y \geq -2x + 6
   \]

Now the inequality is \( y \geq -2x + 6 \), which represents the region **above** the line \( y = -2x + 6 \). The boundary line will be **solid** because the inequality includes \( \geq \) (greater than or equal to).

### Steps to graph:

- **Type of boundary line**: Solid
- **Two points on the boundary line**:
   - When \( x = 0 \), \( y = 6 \), so one point is \( (0, 6) \).
   - When \( x = 3 \), \( y = 0 \), so another point is \( (3, 0) \).

- **Shaded region**: Since the inequality is \( y \geq -2x + 6 \), shade the region **above** the line.

### Summary for the problem:

- **Solid** line.
- Two points on the line: \( (0, 6) \) and \( (3, 0) \).
- Shade region **A** (above the line).

Would you like more details or have any questions?

Here are 5 related questions you might want to explore:

1. How do you determine whether to shade above or below the line for linear inequalities?
2. What happens if the inequality is \( < \) or \( > \) instead of \( \leq \) or \( \geq \)?
3. How do you graph inequalities when the slope is a fraction?
4. Can you graph inequalities in 3-dimensional space?
5. How does changing the inequality sign affect the graph?

**Tip**: Always remember to reverse the inequality when multiplying or dividing by a negative number!

Learn how to solve and graph the linear inequality -3y + 18 <= 6x. This problem involves isolating y, determining the slope, and graphing the boundary line with solid shading above the line for y >= -2x + 6. Suitable for students in Grades 9-12.

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