To find the slope of line \( e \) that is perpendicular to line \( d \) with a slope of \( -\frac{31}{1} \), we use the property that the slopes of two perpendicular lines are negative reciprocals of each other.
The slope of line \( d \) (let's denote it as \( m_d \)) is:
\[ m_d = -31 \]
To find the slope of line \( e \) (let's denote it as \( m_e \)), we calculate the negative reciprocal of \( m_d \):
\[ m_e = -\frac{1}{m_d} = -\frac{1}{-31} = \frac{1}{31} \]
Therefore, the slope of line \( e \) is:
\[ \boxed{\frac{1}{31}} \]