https://file.aiquickdraw.com/mathbot/file/1726701048651inirslk1.jpg

The graph shows a vertical line. A vertical line has no change in the x-coordinate, meaning the rise (change in y) occurs without any corresponding run (change in x). Since slope is calculated as:

\[
\text{slope} = \frac{\Delta y}{\Delta x}
\]

and \(\Delta x = 0\) for vertical lines, the slope of a vertical line is **undefined** because division by zero is not possible.

Thus, the slope of the line is **undefined**.

Would you like more details on this, or have any further questions?

Here are five questions that can help expand on this concept:
1. How do you calculate the slope for a horizontal line?
2. What is the slope of a line that passes through points \((2, 3)\) and \((5, 7)\)?
3. Why is the slope of a vertical line undefined mathematically?
4. What is the equation of a vertical line that passes through the point \((3, 2)\)?
5. How does the slope of parallel and perpendicular lines relate?

**Tip**: When working with vertical lines, remember their equations are always in the form \(x = c\), where \(c\) is the constant x-value for every point on the line.

Find the slope of the line graphed below.

Learn why the slope of a vertical line is undefined with a step-by-step explanation. Understand the concept of slope, the formula, and how vertical lines differ from other types of lines. Suitable for middle school students in Grades 6-8.

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