solve for the equation of a line that is parallel to x=4 and passes through points (3,2)

The equation \( x = 4 \) represents a vertical line that passes through the point \( (4, y) \) for any value of \( y \). Any line parallel to this will also be a vertical line, meaning its equation will be of the form \( x = c \), where \( c \) is a constant.

Since the line must pass through the point \( (3, 2) \), the equation of the line will be:

\[
x = 3
\]

Thus, the equation of the line parallel to \( x = 4 \) and passing through \( (3, 2) \) is \( x = 3 \).

Would you like more details or have any questions?

Here are five related questions:
1. What is the equation of a line parallel to \( y = 5 \)?
2. How do you determine the equation of a line perpendicular to \( x = 4 \)?
3. How can you find the distance between two vertical lines, such as \( x = 4 \) and \( x = 3 \)?
4. What is the general form of the equation for vertical lines?
5. Can a vertical line have a slope? If not, why?

**Tip:** Vertical lines always have an undefined slope because they do not change in the \( y \)-direction.

Discover how to find the equation of a line parallel to x=4 that passes through the point (3,2). This problem covers the concept of vertical lines and parallel lines, perfect for students in Grades 8-10.

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