To find the equation of a line passing through the point [tex]\((9, -4)\)[/tex] and parallel to the [tex]\(x\)[/tex]-axis, follow the steps below:
1. Understand the properties of lines parallel to the [tex]\(x\)[/tex]-axis:
- A line parallel to the [tex]\(x\)[/tex]-axis has a constant [tex]\(y\)[/tex]-coordinate for all values of [tex]\(x\)[/tex]. This means that the [tex]\(y\)[/tex]-coordinate does not change no matter what the [tex]\(x\)[/tex]-coordinate is.
- Therefore, the equation of a line parallel to the [tex]\(x\)[/tex]-axis will be in the form [tex]\(y = c\)[/tex], where [tex]\(c\)[/tex] is a constant.
2. Identify the given point:
- The given point is [tex]\((9, -4)\)[/tex].
3. Determine the equation:
- Since the [tex]\(y\)[/tex]-coordinate of the given point is [tex]\(-4\)[/tex], and the line is parallel to the [tex]\(x\)[/tex]-axis, the [tex]\(y\)[/tex]-coordinate remains constant for all [tex]\(x\)[/tex]-values.
- Therefore, the equation of the line is [tex]\(y = -4\)[/tex].
Thus, the equation of the line passing through the point [tex]\((9, -4)\)[/tex] and parallel to the [tex]\(x\)[/tex]-axis is:
[tex]\[
y = -4
\][/tex]
