Question

4.) a(3, -1)
a.) parallel to the y - axis
b.) perpendicular to the y - axis

Explanation:

Step1: Recall line - axis relationships

A line parallel to the y - axis has the equation of the form $x = k$, where $k$ is a constant. Given the point $A(3,-1)$, for a line parallel to the y - axis passing through this point, the x - coordinate remains the same for all points on the line. So the equation of the line parallel to the y - axis is $x = 3$.
A line perpendicular to the y - axis is parallel to the x - axis and has the equation of the form $y=k$. For a line perpendicular to the y - axis passing through the point $A(3,-1)$, the y - coordinate remains the same for all points on the line. So the equation of the line perpendicular to the y - axis is $y=-1$.

Answer:

a. The equation of the line parallel to the y - axis is $x = 3$.
b. The equation of the line perpendicular to the y - axis is $y=-1$.