find the slope of the line passing through the points $(-9, -6)$ and $(-4, 5)$.

Explanation:

Step1: Identify the formula for slope

The formula for the slope (m) between two points ((x_1,y_1)) and ((x_2,y_2)) is (m=\frac{y_2 - y_1}{x_2 - x_1}).

Step2: Assign values to (x_1,y_1,x_2,y_2)

Here, (x_1=-9,y_1 = - 6,x_2=-4,y_2 = 5).

Step3: Substitute values into the formula

[ \begin{align*} m&=\frac{5-(-6)}{-4-(-9)}\ &=\frac{5 + 6}{-4 + 9}\ &=\frac{11}{5} \end{align*} ]

Answer:

(\frac{11}{5})