To find the slope of the line that passes through the points [tex]\((7, -9)\)[/tex] and [tex]\((6, -11)\)[/tex], we use the formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
### Step-by-Step Solution:
1. Identify the coordinates of the two points:
[tex]\[
(x_1, y_1) = (7, -9)
\][/tex]
[tex]\[
(x_2, y_2) = (6, -11)
\][/tex]
2. Calculate the difference in the y-coordinates ([tex]\( \Delta y \)[/tex]):
[tex]\[
\Delta y = y_2 - y_1 = -11 - (-9) = -11 + 9 = -2
\][/tex]
3. Calculate the difference in the x-coordinates ([tex]\( \Delta x \)[/tex]):
[tex]\[
\Delta x = x_2 - x_1 = 6 - 7 = -1
\][/tex]
4. Substitute these differences into the slope formula:
[tex]\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{-2}{-1} = 2
\][/tex]
### Final Answer:
The slope of the line that passes through the points [tex]\((7, -9)\)[/tex] and [tex]\((6, -11)\)[/tex] is:
[tex]\[
\boxed{2}
\][/tex]
