Let's determine the slope of the line passing through the two points [tex]\((5, 12)\)[/tex] and [tex]\((5, -13)\)[/tex].
1. Identify the coordinates of the points:
- Point 1: [tex]\((x1, y1) = (5, 12)\)[/tex]
- Point 2: [tex]\((x2, y2) = (5, -13)\)[/tex]
2. Calculate the differences in [tex]\(x\)[/tex] and [tex]\(y\)[/tex]:
- [tex]\( \Delta x = x2 - x1 = 5 - 5 = 0 \)[/tex]
- [tex]\( \Delta y = y2 - y1 = -13 - 12 = -25 \)[/tex]
3. Determine the slope:
- The slope [tex]\(m\)[/tex] is given by the formula [tex]\( m = \frac{\Delta y}{\Delta x} \)[/tex].
- Since [tex]\( \Delta x = 0 \)[/tex], we have a division by zero, which means the slope is undefined.
Therefore, the word that describes the slope of the line passing through the points [tex]\((5, 12)\)[/tex] and [tex]\((5, -13)\)[/tex] is Undefined.
The correct answer is [tex]\( \boxed{\text{A. Undefined}} \)[/tex].
