Video: Finding the Equation of a Straight Line Parallel to the 𝑦-Axis

Video Transcript

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

A line that’s parallel to the 𝑦-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 𝑥-axis at some value 𝑎 is of the form 𝑥 equals 𝑎, where 𝑎 is constant. So we’re going to look at each of our equations and make 𝑥 the subject.

Let’s take equation (A). To make 𝑥 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 𝑥 equals nine. Next, we divide through by five, giving us 𝑥 is equal to nine-fifths. This is indeed of the form 𝑥 equals some constant value. So we can say that 𝑎 must represent a line that’s parallel to the 𝑦-axis.

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