To determine which equation represents a line parallel to the [tex]\(x\)[/tex]-axis, let's analyze the properties of each given equation.
1. Equation [tex]\(x = 4\)[/tex]:
- This equation states that [tex]\(x\)[/tex] is always 4, regardless of the value of [tex]\(y\)[/tex].
- This describes a vertical line at [tex]\(x = 4\)[/tex].
- A vertical line is perpendicular, not parallel, to the [tex]\(x\)[/tex]-axis.
2. Equation [tex]\(x + y = 0\)[/tex]:
- Rearranging the equation gives [tex]\(y = -x\)[/tex].
- This represents a line with a slope of -1.
- Lines with a slope other than 0 are not parallel to the [tex]\(x\)[/tex]-axis.
3. Equation [tex]\(x = y\)[/tex]:
- This can also be written as [tex]\(y = x\)[/tex].
- It represents a line with a slope of 1.
- Lines with a slope other than 0 are not parallel to the [tex]\(x\)[/tex]-axis.
4. Equation [tex]\(y = 4\)[/tex]:
- This equation states that [tex]\(y\)[/tex] is always 4, regardless of the value of [tex]\(x\)[/tex].
- This describes a horizontal line at [tex]\(y = 4\)[/tex].
- A horizontal line is parallel to the [tex]\(x\)[/tex]-axis.
Given these properties, the equation that represents a line parallel to the [tex]\(x\)[/tex]-axis is:
[tex]\[ \boxed{D} \ y=4 \][/tex]
