To find the slope of line \( k \) that is perpendicular to line \( j \), we first need to determine the slope of line \( j \) from its equation.
The equation of line \( j \) is given as: \[ y = -\frac{73}{30}x + \frac{88}{51} \]
From this equation, we can identify the slope (\( m_j \)) of line \( j \): \[ m_j = -\frac{73}{30} \]
The slope of a line that is perpendicular to another line is the negative reciprocal of the original slope. Therefore, to find the slope (\( m_k \)) of line \( k \), we calculate the negative reciprocal of \( m_j \): \[ m_k = -\frac{1}{m_j} = -\frac{1}{-\frac{73}{30}} = \frac{30}{73} \]
Thus, the slope of line \( k \) is: \[ \boxed{\frac{30}{73}} \]