Questions: Find the slope, if it exists, of the line containing the pair of points (9,-2) and (9,-6). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope of the line is . (Simplify your answer.) B. The slope is undefined.

Find the slope, if it exists, of the line containing the pair of points (9,-2) and (9,-6). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope of the line is . (Simplify your answer.) B. The slope is undefined.
Transcript text: Find the slope, if it exists, of the line containing the pair of points $(9,-2)$ and $(9,-6)$. Select the correct choice bellow and, if necessary, fill in the answer box to complete your choice. A. The slope of the line is $\square$ . (Simplify your answer.) B. The slope is undefined.
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Solution

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Solution Steps

Step 1: Identify the Points

The given points are \( (9, -2) \) and \( (9, -6) \).

Step 2: Check the x-coordinates

Both points have the same x-coordinate, which is \( x = 9 \). This indicates that the line is vertical.

Step 3: Determine the Slope

For a vertical line, the slope is defined as undefined. This is because the slope formula is given by:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Since \( x_1 = x_2 \), the denominator becomes zero, leading to an undefined slope.

Final Answer

The slope is undefined, so the answer is B.

\(\boxed{\text{undefined}}\)

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