Circle the equation of the line that is parallel to the 𝑦-axis. Is it 𝑥 equals negative two, 𝑦 equals zero, 𝑦 minus 𝑥 equals zero, or 𝑦 plus 𝑥 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 𝑥 is equal to some number. And that number can be found by looking for the value at where the line crosses the 𝑥-axis. This line crosses the 𝑥-axis at 𝑎. So 𝑥 is equal to this number 𝑎. We could also have this line. This would have the equation 𝑥 is equal to negative 𝑏.
We can see in our list that the only equation that looks like these two is this one, 𝑥 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 𝑥-axis. The line 𝑦 minus 𝑥 equals zero is this one. This is because we can form an equation for 𝑦 in terms of 𝑥 by adding extra both sides. That tells us that 𝑦 is equal to 𝑥. So it’s the line that consists of all coordinates where the 𝑦-coordinate is equal to the 𝑥-coordinate.
And this diagonal line sloping downwards is the line 𝑦 plus 𝑥 equals one. We could rearrange this equation by subtracting 𝑥 from both sides. And we see that it’s the same as 𝑦 equals one minus 𝑥. 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 𝑥 equals negative two.