To find the slope of the line that passes through the points \((-5.5, 6.1)\) and \((-2.5, 3.1)\), we can use the formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, we can assign the points:
- \((x_1, y_1) = (-5.5, 6.1)\)
- \((x_2, y_2) = (-2.5, 3.1)\)
Now substitute the values into the slope formula:
\[ m = \frac{3.1 - 6.1}{-2.5 - (-5.5)} \]
Calculate the numerator and the denominator:
Numerator:
\[ 3.1 - 6.1 = -3.0 \]
Denominator:
\[ -2.5 - (-5.5) = -2.5 + 5.5 = 3.0 \]
Now substitute these values back into the slope formula:
\[ m = \frac{-3.0}{3.0} = -1 \]
Thus, the slope of the line that passes through the points \((-5.5, 6.1)\) and \((-2.5, 3.1)\) is \(\boxed{-1}\).
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