To find the equation of a line that passes through the point [tex]\((1,2)\)[/tex] and is parallel to the [tex]\(x\)[/tex]-axis, follow these steps:
1. Identify the characteristics of a line parallel to the [tex]\(x\)[/tex]-axis: A line parallel to the [tex]\(x\)[/tex]-axis runs horizontally. This means that no matter the value of [tex]\(x\)[/tex], the [tex]\(y\)[/tex]-coordinate remains constant.
2. Determine the constant [tex]\(y\)[/tex]-coordinate: Since the line is horizontal and must pass through the point [tex]\((1,2)\)[/tex], the [tex]\(y\)[/tex]-coordinate of every point on this line will be the same as the [tex]\(y\)[/tex]-coordinate of the given point. The [tex]\(y\)[/tex]-coordinate of the given point is 2.
3. Formulate the equation of the line: Given that the [tex]\(y\)[/tex]-coordinate is always 2, the line’s equation is of the form [tex]\(y = k\)[/tex], where [tex]\(k\)[/tex] is a constant. Here, [tex]\(k = 2\)[/tex].
Thus, the equation of the line that passes through the point [tex]\((1,2)\)[/tex] and is parallel to the [tex]\(x\)[/tex]-axis is:
[tex]\[ y = 2 \][/tex]
Among the options provided:
A. [tex]\(y = 1\)[/tex]
B. [tex]\(x = 1\)[/tex]
C. [tex]\(x = 2\)[/tex]
D. [tex]\(y = 2\)[/tex]
The correct choice is D. [tex]\(y = 2\)[/tex].
