The problem involves finding the x-intercept of a line that is parallel to a given line and passes through a specified point [tex]\((-6, 10)\)[/tex].
To solve this, we needs to follow these steps:
1. Determine the slope of the given line:
- The line parallel to the given line has the same slope as the given line. Since the line is parallel to the x-axis, its slope ([tex]\(m\)[/tex]) is zero.
2. Equation of the line:
- The general form of the linear equation is [tex]\( y = mx + b \)[/tex].
- Given that [tex]\(m = 0\)[/tex], the equation simplifies to [tex]\( y = b \)[/tex].
3. Find the y-intercept ([tex]\(b\)[/tex]):
- We are given the point [tex]\((-6, 10)\)[/tex] which the line passes through.
- Substitute this point into the simplified equation [tex]\( y = b \)[/tex]:
[tex]\[ 10 = b \][/tex]
- Therefore, [tex]\(b = 10\)[/tex].
4. Final equation of the line:
- The equation of the line is [tex]\( y = 10 \)[/tex].
5. Determine the x-intercept:
- The x-intercept is found by setting [tex]\( y = 0 \)[/tex] and solving for [tex]\( x \)[/tex]:
[tex]\[ 0 = 10 \][/tex]
- This equation has no solution, indicating that the line [tex]\( y = 10 \)[/tex] is parallel to the x-axis and does not intersect it.
Therefore, none of the given choices [tex]\((6,0)\)[/tex], [tex]\((0,6)\)[/tex], [tex]\((-5,0)\)[/tex], or [tex]\((0,-5)\)[/tex] are the correct answer since they do not lie on the line [tex]\( y = 10 \)[/tex].
Hence, the correct answer is:
```
None
```
