https://file.aiquickdraw.com/mathbot/file/1728485635408cluj4a9t.jpg

The line shown in the graph is vertical, passing through the points \((-4, 5)\) and \((-4, 2)\). 

For a vertical line, the x-coordinate remains constant, while the y-coordinate changes. Since the slope (m) is calculated by the formula:

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

Where \((x_1, y_1)\) and \((x_2, y_2)\) are any two points on the line, for this case:

- \(x_1 = x_2 = -4\)
- \(y_1 = 5\), \(y_2 = 2\)

The denominator \((x_2 - x_1)\) becomes 0, which makes the slope undefined for vertical lines. Therefore, **the slope of this line is undefined**.

Would you like more details on how slope works for different types of lines, or do you have any questions?

Here are five related questions for further exploration:
1. What is the slope of a horizontal line?
2. How do you find the slope between two non-vertical points?
3. Can a vertical line be expressed in slope-intercept form (\(y = mx + b\))?
4. What real-world examples involve vertical lines?
5. How does slope relate to the angle of a line with the x-axis?

**Tip:** When the x-values of two points are the same, the line is vertical, and its slope is always undefined.

Learn why the slope of a vertical line passing through the points (-4, 5) and (-4, 2) is undefined. This example demonstrates the application of the slope formula and explains how vertical lines behave.

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