To determine the slope of the line given by the equation \( y = (9a + 1)x + 8 \), we need to analyze the components of the equation.
In the slope-intercept form of a line \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we can see that the slope \( m \) for our line is \( 9a + 1 \).
Next, we need to find the value of \( a \) such that the line passes through the point \( (2, 6) \). We can do this by substituting \( x = 2 \) and \( y = 6 \) into the line equation:
\[ 6 = (9a + 1)(2) + 8 \]
Now, simplify the equation:
\[ 6 = 2(9a + 1) + 8 \] \[ 6 = 18a + 2 + 8 \] \[ 6 = 18a + 10 \]
Now, isolate \( a \):
\[ 6 - 10 = 18a \] \[ -4 = 18a \] \[ a = -\frac{4}{18} = -\frac{2}{9} \]
With \( a \) determined, we can now substitute back to find the slope:
\[ m = 9a + 1 \] \[ m = 9\left(-\frac{2}{9}\right) + 1 \] \[ m = -2 + 1 = -1 \]
Therefore, the slope of the line is \(\boxed{-1}\).