To determine the ordered pair for the point on the [tex]\( x \)[/tex]-axis that is on the line parallel to the given line through the point [tex]\((-6, 10)\)[/tex], let's break it down methodically.
1. Identify the significance of the [tex]\( x \)[/tex]-axis intersection:
- A point on the [tex]\( x \)[/tex]-axis has a [tex]\( y \)[/tex]-coordinate of 0, as all points on the [tex]\( x \)[/tex]-axis have this property.
2. Point on the Line Parallel to [tex]\( y = 0 \)[/tex] through [tex]\((-6, 10)\)[/tex]:
- Since the line parallel to the [tex]\( x \)[/tex]-axis through [tex]\((-6, 10)\)[/tex] is considered, the [tex]\( y \)[/tex]-coordinate must be the same as the initial point, i.e., 0.
- So, the new point would be [tex]\((-6, 0)\)[/tex].
3. Determine the horizontal translation:
- Among the choices, the correct translation for the new point on the [tex]\( x \)[/tex]-axis is [tex]\((6,0)\)[/tex]. This means the [tex]\( x \)[/tex]-coordinate must be positive and positioned at [tex]\( 6 \)[/tex], while [tex]\( y \)[/tex]-coordinate will remain [tex]\( 0 \)[/tex].
4. Check Options for Consistency:
- The correct option that stands true for a point on the [tex]\( x \)[/tex]-axis (where the [tex]\( y \)[/tex]-coordinate is 0), and matches the conditions given and analysis is the point [tex]\((6,0)\)[/tex].
Hence, the ordered pair for the point on the [tex]\( x \)[/tex]-axis that is on the line parallel to the given line through the point [tex]\((-6, 10)\)[/tex] is [tex]\((6, 0)\)[/tex].
