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The image shows a question asking for the **slope of the line** that passes through the points (4, -2) and (4, 10). Let's solve this step by step.

### Formula for Slope:
The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:

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

### Given Points:
- Point 1: \( (4, -2) \)
- Point 2: \( (4, 10) \)

Now, applying the coordinates to the slope formula:

\[
m = \frac{10 - (-2)}{4 - 4} = \frac{10 + 2}{0} = \frac{12}{0}
\]

Since division by zero is undefined, the slope of the line is **undefined**. This means the line is **vertical**.

Let me know if you need further details or clarifications!

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Here are five related questions to deepen your understanding:
1. How do you determine the slope of a horizontal line?
2. What is the equation of a vertical line passing through a point?
3. How can you graph a line with an undefined slope?
4. What is the slope of a line parallel to the y-axis?
5. Can the slope of a line ever be negative if the line is vertical?

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

What is the slope of the line that passes through the points (4, -2) and (4, 10)? Write your answer in simplest form.

Discover how to calculate the slope of a line that passes through the points (4, -2) and (4, 10). Learn key concepts in coordinate geometry and understand why the slope is undefined for vertical lines.

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