To find the slope of line v, which is perpendicular to line u, we first need to know the slope of line u.
The slope of line u is given by the equation \( y = \frac{3}{7}x + 8 \). This means the slope \( m_u \) of line u is \( \frac{3}{7} \).
When two lines are perpendicular, the slopes \( m_1 \) and \( m_2 \) of those lines satisfy the equation:
\[ m_1 \cdot m_2 = -1 \]
In this case, let \( m_v \) be the slope of line v. So we have:
\[ \frac{3}{7} \cdot m_v = -1 \]
To find \( m_v \), we can solve for \( m_v \):
\[ m_v = -\frac{1}{\frac{3}{7}} = -1 \cdot \frac{7}{3} = -\frac{7}{3} \]
Thus, the slope of line v is
\[ \boxed{-\frac{7}{3}} \]
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