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The question in your image is asking for the equation of a line passing through two points: \( (2, -3) \) and \( (2, 6) \).

These two points have the same \( x \)-coordinate (2), which means the line is **vertical**. A vertical line has an equation of the form:

\[
x = \text{constant}
\]

Since the \( x \)-coordinate for both points is \( 2 \), the equation of the line is:

\[
x = 2
\]

This is the equation of the line that passes through the points \( (2, -3) \) and \( (2, 6) \).

Let me know if you want further details or have any questions!

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Here are 5 related questions to expand your understanding:

1. What is the equation of a horizontal line passing through the point \( (3, 5) \)?
2. How do you find the equation of a line passing through two distinct points?
3. What is the slope of a vertical line, and why is it considered undefined?
4. How does the equation of a vertical line differ from that of a non-vertical line?
5. How would you find the distance between two points like \( (2, -3) \) and \( (2, 6) \)?

**Tip:** When two points have the same \( x \)-coordinate, the line is vertical. If they have the same \( y \)-coordinate, the line is horizontal!

What is an equation of the line that passes through the points (2, -3) and (2, 6)?

Learn how to find the equation of a vertical line passing through the points (2, -3) and (2, 6). This problem involves key concepts in coordinate geometry, including equations of lines and the vertical line theorem. Suitable for students in Grades 9-10.

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