To find the equation of the line that is perpendicular to [tex]\( y = \frac{1}{5} \)[/tex] and passes through the point [tex]\((-4, -3)\)[/tex], follow these steps:
1. Understand the properties of the given line:
- The equation [tex]\( y = \frac{1}{5} \)[/tex] represents a horizontal line because the y-coordinate is constant and equal to [tex]\(\frac{1}{5}\)[/tex].
2. Determine the properties of the perpendicular line:
- A line perpendicular to a horizontal line must be vertical.
- Vertical lines have the equation of the form [tex]\( x = \text{constant} \)[/tex].
3. Use the given point [tex]\((-4, -3)\)[/tex] to find the specific vertical line:
- Since the perpendicular line passes through the point [tex]\((-4, -3)\)[/tex], the x-coordinate of every point on this line must be [tex]\(-4\)[/tex].
4. Write the equation of the perpendicular line:
- Thus, the equation of the line that is perpendicular to [tex]\( y = \frac{1}{5} \)[/tex] and passes through the point [tex]\((-4, -3)\)[/tex] is [tex]\( x = -4 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{A. \ x = -4} \][/tex]
