The given equation is
\[ y = -\frac{14}{7}x + 9. \]
First, we can simplify the fraction \(-\frac{14}{7}\):
\[ -\frac{14}{7} = -2. \]
This means we can rewrite the equation as:
\[ y = -2x + 9. \]
In the slope-intercept form of a linear equation \(y = mx + b\), \(m\) represents the slope. Here, \(m = -2\).
Thus, the slope of the line is
\[ \boxed{-2}. \]