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

# Question Video: Finding the Equation of a Straight Line Parallel to the π¦-Axis Mathematics

Which of the following equations represents a line parallel to the π¦-axis? [A] 5π₯ β 9 = 0 [B] β3π₯ + 9π¦ = 0 [C] 9π₯ + π¦ = β4 [D] 7π₯ + 6π¦ = 4

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### 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 thatβs 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 weβre going to look at each of our equations and make π₯ the subject.

Letβs 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 thatβs parallel to the π¦-axis.

Letβs 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).

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