### Video Transcript

Circle the equation of the line that is parallel to the π¦-axis. Is it π₯ equals negative two, π¦ equals zero, π¦ minus π₯ equals zero, or π¦ plus π₯ equals one?

Letβs remind ourselves what a line is parallel to the π¦-axis would look like. This is one example. A common mistake here is to think that because the line travels in the same direction as the π¦-axis, it is π¦ is equal to some number. In fact, this is not true. The equation of this line is π₯ is equal to some number. And that number can be found by looking for the value at where the line crosses the π₯-axis. This line crosses the π₯-axis at π. So π₯ is equal to this number π. We could also have this line. This would have the equation π₯ is equal to negative π.

We can see in our list that the only equation that looks like these two is this one, π₯ is equal to negative two. In fact, the line π¦ equals zero is a horizontal line that passes through π¦ at zero. Itβs another way of describing the π₯-axis. The line π¦ minus π₯ equals zero is this one. This is because we can form an equation for π¦ in terms of π₯ by adding extra both sides. That tells us that π¦ is equal to π₯. So itβs the line that consists of all coordinates where the π¦-coordinate is equal to the π₯-coordinate.

And this diagonal line sloping downwards is the line π¦ plus π₯ equals one. We could rearrange this equation by subtracting π₯ from both sides. And we see that itβs the same as π¦ equals one minus π₯. This line has a π¦-intercept. It passes through the π¦-axis at one. And it has a gradient of negative one. It slopes downwards.

The equation of the line that is parallel to the π¦-axis is π₯ equals negative two.