The equation $x = 3$ is a vertical line. Lines parallel to vertical lines are also vertical lines and have equations of the form $x = k$, where $k$ is a constant.

Since the line must pass through the point $(-4, 3)$, we use the $x$-coordinate of this point for the equation of the line. Therefore, the equation of the line parallel to $x = 3$ and passing through $(-4, 3)$ is:

$x = -4$

Would you like further details or have any questions?

Here are five related questions:

1. What is the slope of a vertical line?
2. How do you find the equation of a line parallel to $y = 2x + 1$?
3. What is the equation of a line passing through (2, 3) and parallel to $y = -x + 4$?
4. How do you determine if two lines are parallel?
5. What is the distance between the lines $x = -4$ and $x = 3$?

Tip: To determine if two lines are parallel, check if they have the same slope. Vertical lines are always parallel to other vertical lines, and horizontal lines are always parallel to other horizontal lines.