To find the slope of a line that passes through two points, we use the formula for slope \( m \):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
In this case, the points given are \( (1, -7) \) and \( (1, 13) \).
Assigning the coordinates:
- \( (x_1, y_1) = (1, -7) \)
- \( (x_2, y_2) = (1, 13) \)
Now, we can substitute the coordinates into the slope formula:
\[ m = \frac{13 - (-7)}{1 - 1} \] \[ m = \frac{13 + 7}{1 - 1} \] \[ m = \frac{20}{0} \]
Since division by zero is undefined, this means that the slope of the line is undefined.
Thus, the line is vertical because both points have the same x-coordinate.
The answer is that the slope is undefined.