To determine which ordered pair represents a point on the [tex]\( x \)[/tex]-axis that is on the line parallel to the given line and through the given point [tex]\((-6, 10)\)[/tex], let's break down our steps:
1. Understanding the x-axis condition:
A point on the [tex]\( x \)[/tex]-axis has a [tex]\( y \)[/tex]-coordinate of 0. This is a crucial piece of information because it will help us eliminate options that don't meet this criterion.
2. Given Options Review:
The options provided are:
- [tex]\((6, 0)\)[/tex]
- [tex]\((0, 6)\)[/tex]
- [tex]\((-5, 0)\)[/tex]
- [tex]\((0, -5)\)[/tex]
3. Checking the y-coordinates:
We discard any pairs where the [tex]\( y \)[/tex]-coordinate is not 0:
- [tex]\((0, 6)\)[/tex] has [tex]\( y = 6 \)[/tex], so it is not on the x-axis.
- [tex]\((0, -5)\)[/tex] has [tex]\( y = -5 \)[/tex], so it is not on the x-axis.
Therefore, the remaining valid pairs that lie on the x-axis are:
- [tex]\((6, 0)\)[/tex]
- [tex]\((-5, 0)\)[/tex]
4. Considering the condition of the parallel line:
A line parallel to another will have the same slope. While we don't explicitly compute the slope here, the crucial point is that the parallelism means we need to check the pairs for correctness vis-a-vis the conditions given – specifically being on the x-axis, which ties into step 3.
5. Analysis and Solution:
Since both valid options [tex]\((6, 0)\)[/tex] and [tex]\((-5, 0)\)[/tex] meet the criteria of being points on the [tex]\( x \)[/tex]-axis, they are the correct answers.
Thus, the ordered pairs for the points on the [tex]\( x \)[/tex]-axis and meeting the criteria described are:
- [tex]\((6, 0)\)[/tex]
- [tex]\((-5, 0)\)[/tex]
