To identify the slope of the line represented by the equation \( y - 3.5 = -2(x + 1) \), we can first manipulate the equation to its slope-intercept form, \( y = mx + b \), where \( m \) is the slope.
Starting with the given equation:
\[ y - 3.5 = -2(x + 1) \]
Distributing \(-2\) on the right side:
\[ y - 3.5 = -2x - 2 \]
Next, add \( 3.5 \) to both sides:
\[ y = -2x - 2 + 3.5 \]
Simplifying the right side:
\[ y = -2x + 1.5 \]
In this form, we can clearly see that the slope \( m \) is \(-2\).
Thus, the slope of the line is \(\boxed{-2}\).