Question

Theequationoflineuis
y
=
–7
5
x
+ 9
. The
equationoflinevis
y
=
7
5
x
+
6
7
. Are
lineuandlinevparallelorperpendicular?

Answer 1

To determine whether lines \( u \) and \( v \) are parallel or perpendicular, we need to analyze their slopes.

The general equation of a line can be written in the slope-intercept form \( y = mx + b \), where \( m \) is the slope.

1. For line \( u \):
\[
y = -\frac{7}{5}x + 9
\]
The slope (\( m_u \)) of line \( u \) is \( -\frac{7}{5} \).

2. For line \( v \):
\[
y = \frac{7}{5}x + \frac{67}{1}
\]
The slope (\( m_v \)) of line \( v \) is \( \frac{7}{5} \).

Now we compare the slopes:

- Two lines are **parallel** if their slopes are equal, i.e., \( m_u = m_v \).
- Two lines are **perpendicular** if the product of their slopes equals \(-1\), i.e., \( m_u \times m_v = -1 \).

Calculating the product of the slopes:
\[
m_u \times m_v = \left(-\frac{7}{5}\right) \times \left(\frac{7}{5}\right) = -\frac{49}{25}
\]

Since \( -\frac{49}{25} \neq -1 \), the lines are not perpendicular.

Also, since \( -\frac{7}{5} \neq \frac{7}{5} \), the lines are not parallel either.

### Conclusion:
Lines \( u \) and \( v \) are neither parallel nor perpendicular.