To determine which equation represents the vertical line passing through the point [tex]\((1, -9)\)[/tex], we need to understand the characteristics of a vertical line.
A vertical line is a line where all points on the line have the same x-coordinate. As a result, the equation of a vertical line will always be in the form [tex]\(x = a\)[/tex], where [tex]\(a\)[/tex] is the constant x-coordinate of any point the line passes through.
Given the point [tex]\((1, -9)\)[/tex], the x-coordinate is 1. Therefore, the vertical line that passes through this point will have an equation of [tex]\(x = 1\)[/tex].
Now let's examine the given choices:
- A. [tex]\(x = -9\)[/tex]: This represents a vertical line, but it passes through all points where the x-coordinate is [tex]\(-9\)[/tex], not 1.
- B. [tex]\(x = 1\)[/tex]: This is the correct equation since it describes a vertical line passing through all points where the x-coordinate is 1, including the point [tex]\((1, -9)\)[/tex].
- C. [tex]\(y = -9\)[/tex]: This represents a horizontal line passing through all points where the y-coordinate is [tex]\(-9\)[/tex]. It is incorrect for a vertical line.
- D. [tex]\(y = 1\)[/tex]: This represents a horizontal line passing through all points where the y-coordinate is 1. It is also incorrect for a vertical line.
Thus, the correct equation for the vertical line passing through the point [tex]\((1, -9)\)[/tex] is:
[tex]\[ \boxed{2} \ (i.e., \ x = 1) \][/tex]
