Let's solve the problem step by step.
### Part 1: Slope of Line \( I \)
1. Line \( I \) is parallel to the line \( y = -3x - 2 \).
- When two lines are parallel, they have the same slope.
2. Identify the slope of the given line \( y = -3x - 2 \).
- The equation of the line \( y = mx + b \) indicates that \( m \) is the slope.
- In the equation \( y = -3x - 2 \), the slope \( m \) is \(-3\).
3. Therefore, the slope of Line \( I \) is \(-3\).
### Part 2: Slope of Line \( n \)
1. Line \( n \) is perpendicular to the line \( y = \frac{3}{2}x + 8 \).
- When two lines are perpendicular, the slope of one line is the negative reciprocal of the slope of the other line.
2. Identify the slope of the given line \( y = \frac{3}{2}x + 8 \).
- The equation of the line \( y = mx + b \) indicates that \( m \) is the slope.
- In the equation \( y = \frac{3}{2}x + 8 \), the slope \( m \) is \(\frac{3}{2}\).
3. Find the negative reciprocal of \(\frac{3}{2}\).
- The reciprocal of \(\frac{3}{2}\) is \(\frac{2}{3}\).
- The negative reciprocal is \(-\frac{2}{3}\).
4. Therefore, the slope of Line \( n \) is \(-\frac{2}{3}\).
### Final Answers
1. The slope of line \( I \) is \( -3 \).
2. The slope of line [tex]\( n \)[/tex] is [tex]\( -\frac{2}{3} \)[/tex].
