Question

select the correct answer. which equation represents the line that is perpendicular to y = 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 with a slope of $m_1 = 0$. A line perpendicular to a horizontal line is a vertical line. The slope of a vertical line is undefined.

Step2: Determine the equation of the perpendicular line

The equation of a vertical line is of the form $x = k$, where $k$ is a constant. Since the line passes through the point $(-6,-9)$, and for a vertical line all $x$-coordinates are the same, the value of $k$ is the $x$-coordinate of the given point. So $k=-6$.

Answer:

B. $x = - 6$