https://file.aiquickdraw.com/mathbot/file/1726941517360lwtblqu0.jpg

To solve the problem in the image, we are asked to determine for what value of \( x \) the line passing through the given points will be vertical.

The points provided are:
- \( M(x - 5, 6) \)
- \( N(-3, 7) \)

A line is vertical when the \( x \)-coordinates of the two points are equal. So, for the line to be vertical, the \( x \)-coordinate of point \( M \) (which is \( x - 5 \)) must equal the \( x \)-coordinate of point \( N \), which is \( -3 \).

### Step-by-Step Solution:

Set the \( x \)-coordinates equal to each other:
\[
x - 5 = -3
\]

Solve for \( x \):
\[
x = -3 + 5 = 2
\]

### Final Answer:
The value of \( x \) that makes the line vertical is \( x = 2 \).

Would you like further details or have any questions about the steps?

Here are 5 related questions you might find helpful:
1. How do you determine if a line is horizontal?
2. How do you calculate the slope of a line between two points?
3. What is the equation of a vertical line passing through a given point?
4. How does the distance between two points change if a line is vertical?
5. Can you find the midpoint between the points \( M \) and \( N \)?

**Tip:** A vertical line always has an undefined slope because the change in \( x \) is zero, which would make division by zero occur in the slope formula.

For what value of x will the line passing through the following pairs of points be vertical? M(x - 5, 6) and N(-3, 7)

Solve the problem of determining when the line through points M(x - 5, 6) and N(-3, 7) will be vertical. Key concepts include coordinate geometry and vertical lines. This is ideal for students in Grades 8-10.

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