To determine the equation of a line that passes through the point [tex]\((3,2)\)[/tex] and is parallel to the [tex]\(y\)[/tex]-axis, let's follow these steps:
1. Identify the Characteristics of the Line Parallel to the [tex]\(y\)[/tex]-axis:
- A line parallel to the [tex]\(y\)[/tex]-axis is vertical.
- Vertical lines have equations of the form [tex]\(x = \text{constant}\)[/tex], where the constant is the [tex]\(x\)[/tex]-coordinate of any point that the line passes through.
2. Determine the Correct Equation:
- The given point is [tex]\((3,2)\)[/tex].
- For a line to pass through this point and be parallel to the [tex]\(y\)[/tex]-axis, its equation must be [tex]\(x\)[/tex] equal to the [tex]\(x\)[/tex]-coordinate of this point.
3. Find the Constant:
- The [tex]\(x\)[/tex]-coordinate of the point [tex]\((3,2)\)[/tex] is [tex]\(3\)[/tex].
- Therefore, the equation of the line that passes through the point [tex]\((3,2)\)[/tex] and is parallel to the [tex]\(y\)[/tex]-axis is [tex]\(x = 3\)[/tex].
4. Choose the Correct Option:
- Based on the above steps, the correct option is [tex]\(D\)[/tex].
Hence, the equation of the line that passes through the point [tex]\((3,2)\)[/tex] and is parallel to the [tex]\(y\)[/tex]-axis is:
[tex]\[ \boxed{x = 3} \][/tex]
