To find the slope of the line that passes through the points \((-39, -6)\) and \((-40, -36)\), we can use the formula for the slope \(m\) given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
In our case, let's assign the values:
- \((x_1, y_1) = (-39, -6)\)
- \((x_2, y_2) = (-40, -36)\)
Now, substitute these values into the slope formula:
\[ m = \frac{-36 - (-6)}{-40 - (-39)} \]
First, simplify the terms in the numerator and the denominator:
-
For the numerator: \[ -36 - (-6) = -36 + 6 = -30 \]
-
For the denominator: \[ -40 - (-39) = -40 + 39 = -1 \]
Now substitute these simplified values back into the formula for the slope:
\[ m = \frac{-30}{-1} = 30 \]
Thus, the slope of the line that passes through the points \((-39, -6)\) and \((-40, -36)\) is:
\[ \boxed{30} \]