Question

select the correct answer.
which equation represents the line that is perpendicular to $y = \frac{1}{4}$ and passes through (-6,-9)?
a. $x = -9$
b. $x = -6$
c. $y = -9$
d. $y = -4$

Explanation:

Step1: Analyze the given line

The line \( y = \frac{1}{4} \) is a horizontal line (since it has the form \( y = k \) where \( k \) is a constant). A line perpendicular to a horizontal line is a vertical line. Vertical lines have the equation of the form \( x = c \), where \( c \) is a constant.

Step2: Determine the value of \( c \)

The vertical line passes through the point \( (-6, -9) \). For a vertical line \( x = c \), the \( x \)-coordinate of any point on the line is \( c \). The \( x \)-coordinate of the point \( (-6, -9) \) is \( -6 \), so the equation of the vertical line is \( x = -6 \).

Answer:

B. \( x = -6 \)