The

equation

of

line

*v*

is

*y*
 
=
 
7

8

*x*
 
+
 
2

.
 
The

equation

of

line

*w*

is

*y*
 
=
 
–8

7

*x*
 
+
 
8

.
 
Are

line

*v*

and

line

*w*

parallel

or

perpendicular?

To determine if lines *v* and *w* are parallel or perpendicular, we need to analyze the slopes of each line.

1. **Line *v***:  
   The equation is \( y = \frac{7}{8}x + 2 \), so the slope \( m_v \) of line *v* is \( \frac{7}{8} \).

2. **Line *w***:  
   The equation is \( y = -\frac{8}{7}x + 8 \), so the slope \( m_w \) of line *w* is \( -\frac{8}{7} \).

3. **Checking for Parallel Lines**:  
   Two lines are parallel if they have the same slope. Since \( \frac{7}{8} \neq -\frac{8}{7} \), lines *v* and *w* are **not parallel**.

4. **Checking for Perpendicular Lines**:  
   Two lines are perpendicular if the product of their slopes is \(-1\). Let's calculate the product of \( m_v \) and \( m_w \):

   \[
   m_v \times m_w = \frac{7}{8} \times -\frac{8}{7} = -1
   \]

   Since the product is \(-1\), lines *v* and *w* are **perpendicular**.

### Conclusion:
Lines *v* and *w* are perpendicular.

Would you like further details or have any questions?

---

1. What does it mean geometrically when two lines are perpendicular?
2. How can we determine if two lines are parallel or perpendicular from their slopes?
3. Why is the product of slopes of perpendicular lines equal to -1?
4. What are the conditions for two lines to be neither parallel nor perpendicular?
5. How does the y-intercept affect the orientation of lines on a graph?

**Tip:** When analyzing line relationships, always start by comparing their slopes.

The equation of line *v* is y = 7/8 x + 2. The equation of line *w* is y = –8/7 x + 8. Are line *v* and line *w* parallel or perpendicular?

Discover if the lines y = 7/8x + 2 and y = –8/7x + 8 are parallel or perpendicular by analyzing their slopes. This problem covers key algebraic concepts such as slope-intercept form and perpendicular slope relationships. Suitable for students in Grades 9-11.

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