find the slope of the line passing through the points (-3,7) and (2,-6).

Explanation:

Step1: Identify the formula for slope

The formula for the slope (m) of a line passing through 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)

Let ((x_1,y_1)=(-3,7)) and ((x_2,y_2)=(2,-6)).

Step3: Substitute values into the formula

[ \begin{align*} m&=\frac{-6 - 7}{2-(-3)}\ &=\frac{-13}{2 + 3}\ &=\frac{-13}{5} \end{align*} ]

Answer:

(\frac{-13}{5})