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

Which of the following equations represents a line parallel to the 𝑦-axis? [A] 5𝑥 − 9 = 0 [B] −3𝑥 + 9𝑦 = 0 [C] 9𝑥 + 𝑦 = −4 [D] 7𝑥 + 6𝑦 = 4

01:22

### 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).

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.