Linevhasaslopeof
7
8
.Linewhasaslopeof
–7
4
.	 	Are
linevandlinewparallelorperpendicular?

To determine if two lines are parallel or perpendicular, let's analyze the given slopes of each line.

1. **Line \( v \)** has a slope of \( \frac{7}{8} \).
2. **Line \( w \)** has a slope of \( -\frac{7}{4} \).

### Step 1: Check if the Lines are Parallel
Two lines are **parallel** if they have the **same slope**. Here, the slopes of lines \( v \) and \( w \) are different (\(\frac{7}{8}\) and \(-\frac{7}{4}\)), so they are **not parallel**.

### Step 2: Check if the Lines are Perpendicular
Two lines are **perpendicular** if the product of their slopes is **-1**. We’ll multiply the slopes to check:

\[
\frac{7}{8} \times -\frac{7}{4} = -\frac{49}{32}
\]

Since \(-\frac{49}{32} \neq -1\), the lines are **not perpendicular** either.

### Conclusion
The lines \( v \) and \( w \) are **neither parallel nor perpendicular**.

Would you like further details on why slopes determine parallelism and perpendicularity, or do you have any other questions?

---

1. What are the conditions for two lines to be parallel or perpendicular?
2. How can you find the slope of a line given two points?
3. What does it mean when two lines are neither parallel nor perpendicular?
4. How would the solution change if one line had a slope of 0?
5. Can two vertical lines be perpendicular?

**Tip:** To confirm perpendicularity, always remember to check if the product of the slopes equals -1.

Line v has a slope of 7/8. Line w has a slope of -7/4. Are line v and line w parallel or perpendicular?

Learn how to determine if two lines with slopes 7/8 and -7/4 are parallel or perpendicular. This problem includes step-by-step analysis of slopes and conditions for line relationships. Suitable for students in Grades 8-10.

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