Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
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].
### 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].
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.