To find the slope of the line through the points [tex]\((-11, 5)\)[/tex] and [tex]\((-11, -15)\)[/tex], we use the formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], which is given by:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, the coordinates of the points are:
- [tex]\((x_1, y_1) = (-11, 5)\)[/tex]
- [tex]\((x_2, y_2) = (-11, -15)\)[/tex]
Substituting these coordinates into the slope formula, we have:
[tex]\[ m = \frac{-15 - 5}{-11 - (-11)} \][/tex]
First, simplify the numerator [tex]\(y_2 - y_1\)[/tex]:
[tex]\[ y_2 - y_1 = -15 - 5 = -20 \][/tex]
Next, simplify the denominator [tex]\(x_2 - x_1\)[/tex]:
[tex]\[ x_2 - x_1 = -11 - (-11) = -11 + 11 = 0 \][/tex]
So, the formula becomes:
[tex]\[ m = \frac{-20}{0} \][/tex]
Since division by zero is undefined in mathematics, the slope of the line through the points [tex]\((-11, 5)\)[/tex] and [tex]\((-11, -15)\)[/tex] is undefined.
Therefore, the slope is:
[tex]\[ \text{undefined} \][/tex]
