Absolutely! Let’s solve this step by step.
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## 📌 Key Concepts:
1. Parallel Lines
- Two lines are
parallel if they have the
same slope.
- So, to find the slope of a line
parallel to a given line, just use the
same slope as the given line.
2. Perpendicular Lines
- Two lines are
perpendicular if their slopes are
negative reciprocals of each other.
- That means: if the slope of one line is `m`, the slope of a perpendicular line is `-1/m`.
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##
✔ Part 1: Find the slope of a line
parallel to each given line
> Remember: Parallel → Same slope!
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1) `y = -3/2 x - 1`
- Slope = `-3/2`
- ➤
Answer: `-3/2`
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2) `y = 7/4 x - 4`
- Slope = `7/4`
- ➤
Answer: `7/4`
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3) `y = -x - 2`
- This is the same as `y = -1x - 2`
- Slope = `-1`
- ➤
Answer: `-1`
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4) `y = 4x - 5`
- Slope = `4`
- ➤
Answer: `4`
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##
✔ Part 2: Find the slope of a line
perpendicular to each given line
> Remember: Perpendicular → Negative reciprocal of the slope!
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5) `y = 5x + 1`
- Slope = `5`
- Negative reciprocal = `-1/5`
- ➤
Answer: `-1/5`
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6) `y = 3/4 x - 1`
- Slope = `3/4`
- Negative reciprocal = `-4/3`
- ➤
Answer: `-4/3`
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7) `y = -1/5 x + 2`
- Slope = `-1/5`
- Negative reciprocal = `5` (because `-1 / (-1/5) = 5`)
- ➤
Answer: `5`
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8) `y = -4x - 5`
- Slope = `-4`
- Negative reciprocal = `1/4` (because `-1 / (-4) = 1/4`)
- ➤
Answer: `1/4`
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## 🧾 Final Answers:
Parallel Slopes:
1) `-3/2`
2) `7/4`
3) `-1`
4) `4`
Perpendicular Slopes:
5) `-1/5`
6) `-4/3`
7) `5`
8) `1/4`
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✔ You’re all set! These are the correct slopes based on the rules of parallel and perpendicular lines.
Parent Tip: Review the logic above to help your child master the concept of graphing parallel and perpendicular lines worksheet.
