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?

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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.