To find the slope of line \( g \), which is perpendicular to line \( f \), we first need the slope of line \( f \). The slope of line \( f \) is given as \( -\frac{49}{71} \).
For two lines to be perpendicular, the product of their slopes must equal \( -1 \). If \( m_f \) is the slope of line \( f \) and \( m_g \) is the slope of line \( g \), we have:
\[ m_f \cdot m_g = -1 \]
Substituting the slope of line \( f \):
\[ -\frac{49}{71} \cdot m_g = -1 \]
To solve for \( m_g \), multiply both sides by \( -1 \):
\[ \frac{49}{71} \cdot m_g = 1 \]
Now, divide both sides by \( \frac{49}{71} \):
\[ m_g = \frac{1}{\frac{49}{71}} = \frac{71}{49} \]
Thus, the slope of line \( g \) is
\[ \boxed{\frac{71}{49}} \]