The problem asks for the equations of the vertical and horizontal lines passing through the point $(0,3)$.

Solution:

1. Vertical Line Equation:
   A vertical line always has the equation $x = a$, where $a$ is the x-coordinate of the given point.

   • Since the given point is $(0,3)$, the vertical line is:
     $x = 0$

2. Horizontal Line Equation:
   A horizontal line always has the equation $y = b$, where $b$ is the y-coordinate of the given point.

   • Since the given point is $(0,3)$, the horizontal line is:
     $y = 3$

Thus, the answers to enter are:

• Vertical line: $x = 0$
• Horizontal line: $y = 3$

Would you like a deeper explanation or a graph to visualize the lines?

Related Questions:

1. What is the general equation of a vertical and a horizontal line?
2. How do you determine the equation of a line given a single point?
3. What is the slope of a vertical line? What about a horizontal line?
4. How would the equations change if the given point was $(5, -2)$?
5. Can a vertical or horizontal line be represented in slope-intercept form?

Tip: A vertical line has an undefined slope, while a horizontal line has a slope of 0.