The equation of a line that is parallel to the y-axis has the form:

$x = a$

Where $a$ is the x-coordinate of every point on the line. Since the line passes through the point $(7, 3)$, the x-coordinate for this line is $7$. Therefore, the equation of the line passing through $(7, 3)$ and parallel to the y-axis is:

$x = 7$

Would you like more details on why this is the equation, or do you have any further questions?

Here are 5 related questions:

1. What is the equation of a line passing through $(-4, 5)$ and parallel to the y-axis?
2. How would you find the equation of a line parallel to the x-axis passing through a given point?
3. How do you determine if two lines are parallel based on their equations?
4. What is the slope of a line parallel to the y-axis?
5. What is the general form of a vertical line in 3D space?

Tip: Vertical lines always have equations in the form $x = a$, where $a$ is the constant x-coordinate.