Graph Vertical and Horizontal Lines
So if we’re asked to plot the coordinates one, two, then plotting the point one, negative four would be one on the 𝑥-axis and negative four on the 𝑦, and then plotting the point one, three. So looking at each of these points, we can see that they have one thing in common and that is, their first coordinate is always one. So in other words, that 𝑥-coordinate is always one, so 𝑥 equals one. And if we drew a line through the points that we have plotted, we’ll end up with a straight line going through 𝑥 equal to one on the 𝑥-axis and it will be vertical.
Now let’s look at another set of coordinates. So four, six, so there it is, four on 𝑥 and six on 𝑦, so four across and six up. Then three, six will be three across and six up. And then negative five, six is negative five across, or negative five on the 𝑥, and six up, or six on the 𝑦. Now looking at what each of these coordinates have in common, they all have six as the second coordinate, or we could say as the 𝑦-coordinate. So in this case, 𝑦 equals six.
And if we draw a horizontal line through those points, it passes through the 𝑦-axis at six. So for 𝑥 equals one, everywhere on that line, the 𝑥-coordinate will be equal to one. And for 𝑦 equals six, everywhere on that line, the 𝑦-coordinate will be equal to six.
So this leads us to a bigger discovery and that is, that every single 𝑦 equals some value, we will have a horizontal line, and every 𝑥 equals some value, it will be vertical. And that’s important because most people, when they first start looking at horizontal and vertical graphs, they’ll think “oh well if it’s an 𝑥 equals, then it must follow the same way as the 𝑥-axis”, but we have to be careful with this because actually the 𝑥-axis is every single individual coordinate of 𝑥. So on the 𝑥-axis then, actually, 𝑦 is equal to zero. And if on the 𝑥-axis 𝑦 is equal to zero, then I think you could probably work out. Then on the 𝑦-axis, we know that gives us every 𝑦-coordinate, but the thing that zero is 𝑥. So we know that whenever we have 𝑥 equals some value, we’re going to have a vertical line and whenever we have 𝑦 equals some value, it’s going to be horizontal. Let’s have a go at just sketching some graphs.
So first of all, let’s sketch the graph 𝑦 equals negative five. So we’re looking for where every single coordinate in a straight line will give us a coordinate of 𝑦 equal to negative five. So first of all, we can see on the 𝑦-axis where negative five is. And the only straight line we’ll work, will be going horizontally through that negative five. And we’ll label it to show exactly which that graph is, because otherwise it can get quite confusing when you put several graphs on the same axis. And the other thing I did there, was make sure that the line goes through the whole axis. This is important as we start sketching graphs. Now the next one, 𝑥 equals two. So we’re looking for where the 𝑥-coordinate is two. So on the 𝑥-axis where it’s two, we can see is here. And we need every single coordinate to be two. So we know the 𝑦 is a horizontal, the 𝑥 is a vertical, throwing a vertical line through where 𝑥 is equal to two.
And again, we’ve labelled it. Okay. Now looking at the next one, we want where the 𝑦-coordinate is equal to three. So look at the 𝑦-axis and we can see where it’s equal to three. We’re looking for every single coordinate to be 𝑦 equal to three. So we’re gonna draw a straight line through that.
And lastly, 𝑥 equals negative four. So we’re going to look on the 𝑥-axis and we can see where it’s equal to negative four. Again, we want every single coordinate in this line to be 𝑥 equals negative four. So we’re looking for a vertical line through that point.
And there we have it. So every single 𝑥 equals some constant, we’re looking for a vertical line. And every 𝑦 equals, we’re looking for a horizontal.