To find the equation of a line that passes through the point [tex]\((6, -7)\)[/tex] and has a slope of [tex]\(0\)[/tex], follow these steps:
1. Understand the Slope:
- A slope of [tex]\(0\)[/tex] indicates that the line is horizontal. This means that it has no vertical change as it moves from left to right.
2. Horizontal Line Characteristics:
- For a horizontal line, the [tex]\(y\)[/tex]-coordinate remains constant for all [tex]\(x\)[/tex]-values on the line. Therefore, the equation of a horizontal line is always in the form [tex]\(y = c\)[/tex], where [tex]\(c\)[/tex] is a constant.
3. Use the Given Point:
- Since the line passes through the point [tex]\((6, -7)\)[/tex], the [tex]\(y\)[/tex]-coordinate of this point, [tex]\(-7\)[/tex], will be the constant value for the equation of our horizontal line.
4. Write the Equation:
- Because the [tex]\(y\)[/tex]-coordinate is [tex]\(-7\)[/tex] for all points on the line, the equation of the line is simply:
[tex]\[
y = -7
\][/tex]
So, the equation of the line that passes through the point [tex]\((6, -7)\)[/tex] and has a slope of [tex]\(0\)[/tex] is [tex]\(\boxed{y = -7}\)[/tex].
