Video: AQA GCSE Mathematics Higher Tier Pack 5 β€’ Paper 3 β€’ Question 3

Circle the equation of the line that is parallel to the 𝑦-axis. [A] π‘₯ = βˆ’2 [B] 𝑦 = 0 [C] 𝑦 βˆ’ π‘₯ = 0 [D] 𝑦 + π‘₯ = 1

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Video Transcript

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

Let’s remind ourselves what a line is parallel to the 𝑦-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 𝑦-axis, it is 𝑦 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‘Ž. So π‘₯ is equal to this number π‘Ž. We could also have this line. This would have the equation π‘₯ is equal to negative 𝑏.

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 𝑦 equals zero is a horizontal line that passes through 𝑦 at zero. It’s another way of describing the π‘₯-axis. The line 𝑦 minus π‘₯ equals zero is this one. This is because we can form an equation for 𝑦 in terms of π‘₯ by adding extra both sides. That tells us that 𝑦 is equal to π‘₯. So it’s the line that consists of all coordinates where the 𝑦-coordinate is equal to the π‘₯-coordinate.

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

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

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