To find the slope of the line passing through points \( A(5, 6) \) and \( B(15, 12) \), you can use the formula for the slope \( m \):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, \( (x_1, y_1) = (5, 6) \) and \( (x_2, y_2) = (15, 12) \). Plugging in the values:
\[ m = \frac{12 - 6}{15 - 5} = \frac{6}{10} = \frac{3}{5} \]
Thus, the slope of the line \( n \) is \( \frac{3}{5} \).