To find the slope of the line that passes through the points [tex]\((-9, -9)\)[/tex] and [tex]\((-9, -7)\)[/tex], we need to use the formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Given the points [tex]\((-9, -9)\)[/tex] and [tex]\((-9, -7)\)[/tex], we can substitute the values for the coordinates into the formula:
[tex]\[
x_1 = -9, \quad y_1 = -9, \quad x_2 = -9, \quad y_2 = -7
\][/tex]
First, calculate the change in the y-coordinates ([tex]\(\Delta y\)[/tex]):
[tex]\[
\Delta y = y_2 - y_1 = -7 - (-9) = -7 + 9 = 2
\][/tex]
Next, calculate the change in the x-coordinates ([tex]\(\Delta x\)[/tex]):
[tex]\[
\Delta x = x_2 - x_1 = -9 - (-9) = -9 + 9 = 0
\][/tex]
Now, substitute the values of [tex]\(\Delta y\)[/tex] and [tex]\(\Delta x\)[/tex] into the slope formula:
[tex]\[
m = \frac{\Delta y}{\Delta x} = \frac{2}{0}
\][/tex]
The denominator is zero, which means the slope is undefined. This happens because the line is vertical; all points on the line have the same x-coordinate.
In conclusion, the slope of the line that passes through the points [tex]\((-9, -9)\)[/tex] and [tex]\((-9, -7)\)[/tex] is undefined.
