### Video Transcript

Which of the following equations
represents a line parallel to the π¦-axis? Is it (A) five π₯ minus nine equals
zero, (B) negative three π₯ plus nine π¦ equals zero, (C) nine π₯ plus π¦ equals
negative four, or (D) seven π₯ plus six π¦ equals four?

A line thatβs parallel to the
π¦-axis is a vertical line. It might look a little something
like this. And we say that the equation of a
vertical line that passes through the π₯-axis at some value π is of the form π₯
equals π, where π is constant. So weβre going to look at each of
our equations and make π₯ the subject.

Letβs take equation (A). To make π₯ the subject, we perform
a series of inverse operations. First, we want to eliminate
negative nine. So we add nine to both sides. And our equation becomes five π₯
equals nine. Next, we divide through by five,
giving us π₯ is equal to nine-fifths. This is indeed of the form π₯
equals some constant value. So we can say that π must
represent a line thatβs parallel to the π¦-axis.

Letβs consider equations (B), (C),
and (D). Each equation contains both an π₯
and a π¦. And when we rearrange them to make
π₯ the subject, we end up with π₯ being some function of π¦. This tells us that the equations
(B), (C), and (D) represent diagonal lines, not vertical ones. The correct answer is (A).