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The inequality given is:

\[
2x - 3y \leq -12
\]

### Step-by-Step Process to Graph the Inequality:

1. **Rewrite the inequality in slope-intercept form** (i.e., \( y = mx + b \)) for easier graphing:
   
   \[
   2x - 3y \leq -12
   \]
   First, subtract \( 2x \) from both sides:
   \[
   -3y \leq -2x - 12
   \]
   Now, divide everything by \( -3 \). Remember, dividing an inequality by a negative number reverses the inequality sign:
   \[
   y \geq \frac{2}{3}x + 4
   \]
   
   So, the equation of the boundary line is:
   \[
   y = \frac{2}{3}x + 4
   \]

2. **Graph the boundary line**:
   Since the inequality is \( y \geq \frac{2}{3}x + 4 \), this is a solid line (since \( \leq \) includes equality).
   - The slope is \( \frac{2}{3} \), meaning that for every 3 units you move horizontally (to the right), you move 2 units up.
   - The y-intercept is \( 4 \), so the line passes through the point \( (0, 4) \).

3. **Shade the correct region**:
   Since the inequality is \( y \geq \frac{2}{3}x + 4 \), shade **above** the line. This is the region where \( y \) values are greater than or equal to the line.

Would you like me to generate the graph of this inequality? If you have further questions or need details, feel free to ask!

### Related Questions:
1. How do you solve linear inequalities in two variables?
2. What happens to an inequality when you multiply or divide by a negative number?
3. How do you determine the slope and y-intercept of a line?
4. What is the significance of the shaded region in a graph of inequalities?
5. How do you know whether to use a dashed or solid line when graphing inequalities?

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

Learn how to graph the linear inequality 2x - 3y ≤ -12. This step-by-step solution involves converting the inequality to slope-intercept form and shading the appropriate region on the graph. Suitable for students in Grades 8-10.

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