Question

a. find the equation of the line passing through (0, -1) and parallel to the line x = -2. parallel line:
b. find the equation of the line passing through (0, -1) and perpendicular to the line x = -2. perpendicular line:

Explanation:

Step1: Analyze the form of the given line

The line $x = - 2$ is a vertical line. A line parallel to a vertical line is also vertical. The equation of a vertical line is of the form $x = k$, where $k$ is a constant. Since the line passes through the point $(0,-1)$, the $x$-coordinate of all points on the line is $0$. So the equation of the parallel line is $x = 0$.

Step2: Analyze the form of the perpendicular line

A line perpendicular to a vertical line is a horizontal line. The equation of a horizontal line is of the form $y = k$, where $k$ is a constant. Since the line passes through the point $(0,-1)$, the $y$-coordinate of all points on the line is $-1$. So the equation of the perpendicular line is $y=-1$.

Answer:

a. $x = 0$
b. $y=-1$