The slope of line \( g \) is given in the equation \( y = -\frac{6}{7}x + 9 \). From this equation, we can see that the slope (denoted as \( m_g \)) is:
\[ m_g = -\frac{6}{7} \]
For line \( h \), which is perpendicular to line \( g \), the relationship between their slopes is that the product of the slopes of two perpendicular lines equals -1:
\[ m_g \cdot m_h = -1 \]
Let \( m_h \) be the slope of line \( h \). Therefore, we have:
\[ -\frac{6}{7} \cdot m_h = -1 \]
To find \( m_h \), we can solve the equation:
\[ m_h = \frac{-1}{-\frac{6}{7}} = \frac{7}{6} \]
Thus, the slope of line \( h \) is:
\[ m_h = \frac{7}{6} \]
This is the simplified answer for the slope of line \( h \).
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