Answer :
To determine the equation of the line that passes through the point [tex]\((3, 2)\)[/tex] and is parallel to the y-axis, let's analyze the properties of such a line.
1. Understanding the Concept of a Line Parallel to the y-Axis:
- A line that is parallel to the y-axis runs vertically.
- Vertical lines have a constant x-coordinate for all points on the line.
2. Identifying the Key Information:
- We need to find the equation of a vertical line that contains the point [tex]\((3, 2)\)[/tex].
- For a vertical line, the x-coordinate remains the same no matter what the y-coordinate is.
3. Determining the Constant x-Value:
- Since the line passes through the point [tex]\((3, 2)\)[/tex], the x-coordinate for all points on this line will be [tex]\(3\)[/tex].
4. Formulating the Equation:
- The equation of a vertical line is always of the form [tex]\(x = \text{constant}\)[/tex].
Given these steps and understanding, the equation of the line that passes through [tex]\((3, 2)\)[/tex] and is parallel to the y-axis is:
[tex]\[ \boxed{x = 3} \][/tex]
Thus, the correct answer is:
D. [tex]\(x = 3\)[/tex]
1. Understanding the Concept of a Line Parallel to the y-Axis:
- A line that is parallel to the y-axis runs vertically.
- Vertical lines have a constant x-coordinate for all points on the line.
2. Identifying the Key Information:
- We need to find the equation of a vertical line that contains the point [tex]\((3, 2)\)[/tex].
- For a vertical line, the x-coordinate remains the same no matter what the y-coordinate is.
3. Determining the Constant x-Value:
- Since the line passes through the point [tex]\((3, 2)\)[/tex], the x-coordinate for all points on this line will be [tex]\(3\)[/tex].
4. Formulating the Equation:
- The equation of a vertical line is always of the form [tex]\(x = \text{constant}\)[/tex].
Given these steps and understanding, the equation of the line that passes through [tex]\((3, 2)\)[/tex] and is parallel to the y-axis is:
[tex]\[ \boxed{x = 3} \][/tex]
Thus, the correct answer is:
D. [tex]\(x = 3\)[/tex]
