Question

write the equation of a line that is perpendicular to $x = 3$ and that passes through the point $(0, - 4)$.

Explanation:

Step1: Analyze the given line

The line $x = 3$ is a vertical line. A line perpendicular to a vertical line is a horizontal line.

Step2: Recall the form of a horizontal - line equation

The equation of a horizontal line is of the form $y = k$, where $k$ is a constant.

Step3: Determine the value of $k$

Since the line passes through the point $(0,-4)$, and for a horizontal line the $y$ - coordinate is the same for all points on the line, $k=-4$.

Answer:

$y=-4$