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

Which of the following equations represents a line parallel to the 𝑦-axis? [A] 5π‘₯ βˆ’ 9 = 0 [B] βˆ’3π‘₯ + 9𝑦 = 0 [C] 9π‘₯ + 𝑦 = βˆ’4 [D] 7π‘₯ + 6𝑦 = 4

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Video Transcript

Which of the following equations represents a line parallel to the 𝑦-axis? Is it (A) five π‘₯ minus nine equals zero, (B) negative three π‘₯ plus nine 𝑦 equals zero, (C) nine π‘₯ plus 𝑦 equals negative four, or (D) seven π‘₯ 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 π‘₯-axis at some value π‘Ž is of the form π‘₯ equals π‘Ž, where π‘Ž is constant. So we’re going to look at each of our equations and make π‘₯ the subject.

Let’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‘Ž must represent a line that’s parallel to the 𝑦-axis.

Let’s consider equations (B), (C), and (D). Each equation contains both an π‘₯ and a 𝑦. And when we rearrange them to make π‘₯ the subject, we end up with π‘₯ 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).

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