To determine the equation of the horizontal line passing through the point [tex]\((-1, 2)\)[/tex], we need to understand the characteristics of horizontal lines in a Cartesian plane.
### Characteristics of a horizontal line:
1. A horizontal line has a constant [tex]\(y\)[/tex]-value for all points along the line.
2. The [tex]\(y\)[/tex]-value of all the points on the line is equal to the [tex]\(y\)[/tex]-coordinate of the point through which the line passes.
Given the point [tex]\((-1, 2)\)[/tex], the [tex]\(y\)[/tex]-coordinate is 2. Therefore, the horizontal line passing through this point will have a constant [tex]\(y\)[/tex]-value of 2.
This can be expressed using the equation:
[tex]\[ y = 2 \][/tex]
Let's evaluate the given options to identify the correct answer:
- A. [tex]\(x = -1\)[/tex]: This represents a vertical line passing through [tex]\(x = -1\)[/tex], not a horizontal line.
- B. [tex]\(y = -1\)[/tex]: This represents a horizontal line, but it passes through a [tex]\(y\)[/tex]-coordinate of [tex]\(-1\)[/tex], which is incorrect.
- C. [tex]\(x = 2\)[/tex]: This represents a vertical line passing through [tex]\(x = 2\)[/tex], not a horizontal line.
- D. [tex]\(y = 2\)[/tex]: This represents a horizontal line passing through [tex]\(y = 2\)[/tex], which matches the requirement.
Hence, the correct equation that represents the horizontal line passing through the point [tex]\((-1, 2)\)[/tex] is:
[tex]\[ \boxed{y = 2} \][/tex]
So, the correct answer is:
[tex]\[ \text{D. } y = 2 \][/tex]
