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What is the slope of the line that passes through the points (6, 10) and (6,-2)? Write your answer in simplest form.
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To determine the slope of the line that passes through the points \(\((6, 10)\)\) and \(\((6, -2)\)\), follow these steps:

1. Identify the coordinates of the points:
- Point 1: \(\((x_1, y_1) = (6, 10)\)\)
- Point 2: \(\((x_2, y_2) = (6, -2)\)\)

2. Calculate the change in the y-coordinates (\(\(\Delta y\)\)):
\(\[ \Delta y = y_2 - y_1 = -2 - 10 = -12 \]\)

3. Calculate the change in the x-coordinates (\(\(\Delta x\)\)):
\(\[ \Delta x = x_2 - x_1 = 6 - 6 = 0 \]\)

4. Determine the slope using the formula:
\(\[ \text{slope} = \frac{\Delta y}{\Delta x} \]\)

Given that \(\(\Delta x = 0\)\), this means the denominator is zero. A fraction with a zero denominator is undefined.

Therefore, the slope of the line passing through the points \(\((6, 10)\)\) and \(\((6, -2)\)\) is undefined, as the line is vertical.

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