A vertical line cannot be parallel to a line at 45 degrees. Here's why:

• A vertical line has an undefined slope (since its equation is $x = c$, where $c$ is a constant), meaning it is perfectly vertical.

• A line at 45 degrees has a slope of 1, since a line that makes a 45-degree angle with the horizontal has equal rise and run ($y = x + b$).

For two lines to be parallel, they must have the same slope. Since the slopes of a vertical line and a line at 45 degrees are not the same, they cannot be parallel.

Would you like more details or have any questions?

Here are some related questions:

1. What is the equation of a line parallel to a 45-degree line?
2. How do we find the slope of a line given its angle?
3. Can two lines with different slopes ever intersect?
4. What is the condition for two lines to be perpendicular?
5. How do we calculate the angle between two intersecting lines?

Tip: Two lines are parallel if and only if their slopes are equal.