To determine which equation represents the line that is parallel to [tex]\(y = 3\)[/tex] and passes through the point [tex]\((-2, -8)\)[/tex], let's go through the problem step by step.
1. Understanding the given line [tex]\(y = 3\)[/tex]:
- The equation [tex]\(y = 3\)[/tex] is a horizontal line where the y-coordinate is constant at 3 for all values of x.
- This line is parallel to any other horizontal line where the y-coordinate is also constant.
2. Equation of a line parallel to [tex]\(y = 3\)[/tex]:
- A line parallel to [tex]\(y = 3\)[/tex] must also be a horizontal line, meaning it must have a constant y-coordinate.
3. Finding the line that passes through the point [tex]\((-2, -8)\)[/tex]:
- The line we are looking for must go through the point with coordinates [tex]\((-2, -8)\)[/tex].
- Since this line must be parallel to [tex]\(y = 3\)[/tex], it must be a horizontal line.
- A horizontal line passing through [tex]\((-2, -8)\)[/tex] will have the same y-coordinate for all points, which is [tex]\(-8\)[/tex].
4. Formulating the equation of the desired line:
- Therefore, the equation of the line that is parallel to [tex]\(y = 3\)[/tex] and passes through [tex]\((-2, -8)\)[/tex] is [tex]\(y = -8\)[/tex].
5. Choosing the correct option:
- The correct equation is [tex]\(y = -8\)[/tex].
Thus, the answer is:
C. [tex]\(y = -8\)[/tex]
