To determine the equation of a line that is parallel to the \( x \)-axis and passes through the point \((1, 2)\), we need to consider two important aspects: the properties of lines parallel to the \( x \)-axis and the given point.
1. Understanding Lines Parallel to the \( x \)-axis:
- A line that is parallel to the \( x \)-axis is horizontal.
- In mathematical terms, this means that the \( y \)-coordinate for any point on this line remains constant.
2. Given Point:
- The point through which the line passes is \((1, 2)\).
- Here, \(1\) is the \( x \)-coordinate, and \(2\) is the \( y \)-coordinate.
Since the line is parallel to the \( x \)-axis, the \( y \)-coordinate of any point on this line must be the same as the \( y \)-coordinate of the given point. Therefore, the constant \( y \)-coordinate for all points on this line is 2.
Thus, the equation of the line is:
[tex]\[ y = 2 \][/tex]
We now match this equation to the provided options:
- Option A. \( y = 2 \)
- Option B. \( x = 2 \)
- Option C. \( x = 1 \)
- Option D. \( y = 1 \)
The correct answer, which states the proper equation of the line, is Option A: [tex]\( y = 2 \)[/tex].
