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To find the slope of the line passing through the points \((10, -5)\) and \((10, -9)\), we use the slope formula:

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

Here, \((x_1, y_1) = (10, -5)\) and \((x_2, y_2) = (10, -9)\). Plugging these values into the formula:

\[
m = \frac{-9 - (-5)}{10 - 10} = \frac{-9 + 5}{0} = \frac{-4}{0}
\]

Since division by zero is undefined, the slope does not exist. This means the line is **vertical**.

Would you like further details or have any questions?

Here are five related questions you might find useful:
1. What is the equation of a vertical line through a given point?
2. How do you find the slope of a horizontal line?
3. Can a line have both undefined and zero slopes?
4. How does the slope affect the steepness and direction of a line?
5. What is the difference between vertical and horizontal lines in terms of slope?

**Tip:** If the \(x\)-coordinates of two points are the same, the line is vertical, and its slope is undefined.

Find the slope, if it exists, of the line containing the points (10, -5) and (10, -9).

Learn how to find the slope of a line passing through the points (10, -5) and (10, -9). This problem uses the slope formula and explores why division by zero leads to an undefined slope, indicating that the line is vertical. Ideal for students in Grades 8-10.

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