To find the equation of a vertical line passing through a given point, we need to understand the properties of vertical lines. Vertical lines have the same x-coordinate for all points along the line. This means that the x-coordinate does not change, regardless of the y-coordinate.
Given the point [tex]\((-5, -2)\)[/tex], we note that the x-coordinate is [tex]\(-5\)[/tex]. For a vertical line passing through this point, every point on the line will have an x-coordinate of [tex]\(-5\)[/tex], while the y-coordinate can be any value.
Therefore, the equation of the vertical line passing through the point [tex]\((-5, -2)\)[/tex] is simply:
[tex]\[ x = -5 \][/tex]
This equation indicates that no matter what the y-coordinate is, the x-coordinate will always be [tex]\(-5\)[/tex].
