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Let's solve the inequalities and describe how to graph them.

### 3. \( y \geq -x - 6 \)

This inequality represents a line with slope \(-1\) and y-intercept at \(-6\) (point \( (0, -6) \)). 

1. **Plot the boundary line**: First, plot the line \( y = -x - 6 \). Since the inequality is \( \geq \), the boundary line will be solid.
2. **Determine the shaded region**: The inequality means that we are interested in the region where \( y \) is greater than or equal to \( -x - 6 \), so you will shade the region **above** the line.

### 4. \( 2y + 6 < 3x \)

1. First, solve for \( y \) to put it in slope-intercept form:
   \[
   2y < 3x - 6
   \]
   \[
   y < \frac{3}{2}x - 3
   \]
   
2. **Plot the boundary line**: This represents the line \( y = \frac{3}{2}x - 3 \) with slope \( \frac{3}{2} \) and y-intercept at \( -3 \) (point \( (0, -3) \)). Since the inequality is \( < \), the boundary line will be dashed.
3. **Determine the shaded region**: Since the inequality is \( y < \frac{3}{2}x - 3 \), shade the region **below** the dashed line.

### Graphing Tips:
- For problem 3, use a **solid line** and shade above the line.
- For problem 4, use a **dashed line** and shade below the line.

Would you like to go through the detailed graphing steps or need help with anything else? Here are 5 follow-up questions you might consider:

1. How do you graph inequalities that use \( > \) or \( < \) instead of \( \geq \) or \( \leq \)?
2. How do you determine which side of the line to shade when graphing inequalities?
3. How can you find the intersection points of two linear inequalities?
4. What changes when an inequality is flipped (i.e., \( \geq \) becomes \( \leq \))?
5. How do you solve systems of inequalities graphically?

**Tip**: Always test a point (like \( (0,0) \)) to confirm which region to shade if you're unsure!

Graph each inequality: 3. y ≥ -x - 6; 4. 2y + 6 < 3x

Learn how to graph the linear inequalities y ≥ -x - 6 and 2y + 6 < 3x. This involves plotting boundary lines, using solid or dashed lines, and shading the correct regions. Suitable for students in Grades 9-12.

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