Question

Line u passes through points (9, 9) and (2, 13). Line v is perpendicular to u. What is the slope of line v?

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answer 1

To find the slope of line \( v \), we first need to determine the slope of line \( u \), which passes through the points \( (9, 9) \) and \( (2, 13) \).

The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Plugging in our points \( (9, 9) \) (where \( (x_1, y_1) = (9, 9) \)) and \( (2, 13) \) (where \( (x_2, y_2) = (2, 13) \)), we have:

\[
m_u = \frac{13 - 9}{2 - 9} = \frac{4}{-7} = -\frac{4}{7}
\]

Now that we have the slope of line \( u \) as \( -\frac{4}{7} \), we can find the slope of line \( v \). Since line \( v \) is perpendicular to line \( u \), the slope of line \( v \), denoted \( m_v \), is the negative reciprocal of the slope of line \( u \).

The negative reciprocal is calculated as follows:

\[
m_v = -\frac{1}{m_u} = -\frac{1}{-\frac{4}{7}} = \frac{7}{4}
\]

Thus, the slope of line \( v \) is

\[
\boxed{\frac{7}{4}}
\]