Hey, everyone. So up until now, all the graphing and plotting that we've seen in this course have only involved one variable like x, and we've always plotted it on the horizontal number line. But a lot of graphing for the rest of this course is going to involve the relationship between 2 variables. So we're going to have to plot points and also equations. And in order to do that with multiple variables, we'll need to be familiar with the rectangular coordinate system. So that's what we're going to talk about in this video. Basically, what I'm going to show you here is how we can take coordinates that are described with two numbers like 4, 3, and I'm going to show you that these are really just locations on this two-dimensional grid, and it has to do with their x and y values. So I'm going to show you how to plot these kinds of points. So let's get started here. The rectangular coordinate system, sometimes called the Cartesian plane, is really just where you have a horizontal number line and a vertical number line that are sort of together and crossing. These are 2 perpendicular number lines that come together to form a 2-dimensional grid instead of just a one-dimensional line. So now we're going to describe locations not just as an x-coordinate but also as a y-coordinate as well. So let's get into the specifics. This horizontal axis that we've been familiar with so far is called the x-axis, and so you're going to see a little x written out here along this number line. And then over on the vertical axis, that's going to be the y-axis. So, basically, what we can do is now instead of describing just one point on this number line with one number, we can actually describe it using two numbers and one for the x and one for the y. And the way that we ascribe points or sometimes these are called ordered pairs, is basically just a position, and it's always in the form where it has parentheses and there are two numbers, an x and a y. So for example, there's going to be 4, 3. That's an x coordinate and a y coordinate. That's called an ordered pair. Basically, what you're going to do here is you're going to start from the sort of center of this diagram, and you're going to go along the x-axis until you hit 4. So this is going to go 4 in the x, and then you're going to go 3 in the y from there. So that's what the coordinate 4, 3 means. It means you go 4 in the x and then 3 in the y, and that's why this location is equal to 4, 3. Alright? So that's what a point or an ordered pair is. So for this example, we're just going to be plotting out a bunch of ordered pairs on this graph. So let's keep going. Now notice how in b, here, I've got a negative number inside for the x-coordinate. So what does that mean? Well, in order for us to understand that, we'll talk about the origin. The origin really is just the center of this diagram, which we've already sort of labeled over here, and it's just the point 0, 0. It's where your graph starts. It's also basically where the x and y axis intersect. And notice what happens is it also separates positive, sorry, positive and negative values. So for example, what you'll see is that the x values are positive, the y values are positive to the right and above the origin. So x values are positive, and y values are positive to the right and above the origin. And then they're negative when they're to the left or below the origin, as we can see over here. Alright? So how do we graph the coordinates negative 3, 2? Well, now what this is saying is that on the y-axis, we're going to go to negative 3. So instead of going to the right like I did for a, I'm going to have to go to the left, negative 3, and then I have to get to 2 on the y-axis. So do I have to go up or down? Well, I have to get to positive 2, so I'm going to have to go up like this. So this is the point b, and this is negative 3, 2. Alright? Pretty straightforward. Let's keep doing a few more examples. So here we've got negative 2, negative 3. Remember, this is x, y. Here I have to go to negative 2 by going to the left, and then I have to go down to get to negative 3. That's over here. So this is the coordinate c, and this is negative 2, negative 3. Alright. And now we have 5, negative 4. So 5, negative 4 is going to be positive 5. So here, I'm actually going to go to the right. I'm going to have to go to the right 5, and then I have to get to negative 4, so I have to go down from here. So this is 1, 2, 3, and 4. This is negative 4. So this over here is the point d, which is 5, negative 4. Alright? We've got a few more. We've got the 0, 0, but we actually have already seen that before. 0, 0 is really just the origin. So that's just the location 0, 0. And then finally, we've got 0, negative 3. Again, what this means is that you're going to go 0 on the x-axis, so you're not really going to go left or right. Then you're going to have to go down just from the origin until you hit to negative 3. So this is the coordinate f0, negative 3. Alright? So this is a little bit sort of cluttered here. We've got a lot of points, but, hopefully, this makes sense in how to sort of graph them. The last thing I want to talk about here is that a lot of these points have sort of fallen into 2, 4 different corners of this diagram, and these are called quadrants. Basically, what happens is that the x and y axes divide the graph into 4 regions or 4 corners, and these just get names. They're called quadrants. And, basically, they all have numbers, and quadrant 1 is going to stop at the is going to start at the right top right-hand corner, and then you're going to keep going in increasing number as you go counterclockwise around. So this is quadrant 2, this is quadrant 3, and this is quadrant 4. Sometimes they get Roman numerals, but you don't really need to know that. Alright, folks. So that's just an introduction into graphing in the coordinate system. Thanks for watching.
Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
2. Graphs of Equations
Graphs and Coordinates
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