To find the slope of the line that passes through the points \((-5.5, 6.1)\) and \((-2.5, 3.1)\), you can use the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Where \((x_1, y_1) = (-5.5, 6.1)\) and \((x_2, y_2) = (-2.5, 3.1)\).
Plugging in the values:
\[ m = \frac{3.1 - 6.1}{-2.5 - (-5.5)} \]
Calculating the numerator:
\[ 3.1 - 6.1 = -3 \]
Calculating the denominator:
\[ -2.5 + 5.5 = 3 \]
Now substituting these values back into the slope formula:
\[ m = \frac{-3}{3} = -1 \]
Thus, the slope of the line that passes through the given points is \(\boxed{-1}\).