The slope of line \( s \) is given as \( -\frac{9}{7} \).
To find the slope of line \( t \), which is perpendicular to line \( s \), we use the property that the slopes of two perpendicular lines multiply to \(-1\).
Let the slope of line \( t \) be \( m_t \). We have:
\[ m_s \cdot m_t = -1 \]
Substituting the slope of line \( s \):
\[ -\frac{9}{7} \cdot m_t = -1 \]
To find \( m_t \), we can solve for it:
\[ m_t = \frac{-1}{-\frac{9}{7}} = \frac{7}{9} \]
Thus, the slope of line \( t \) is
\[ \boxed{\frac{7}{9}}. \]
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