Constructing the coordinate plane

0:00- [Instructor] What we're gonna think about in this video is given a set of points, how we might wanna set up our x and y-axes to make sure that we have space to fit all these points, and also that we aren't scrunching things together or making it hard to visualize those points.

0:16So what we have are two groups of points here, and I'm going to separately graph these five points on one set of axes and then separately these other five on another set. And if you are inspired, please pause this video and do it yourself. All right, so let's just first look at this first set of points.

0:35And what I like to do is think about the minimum and maximum x values and the minimum and maximum y values. So if I look at the x values, our minimum is, let's see,

0:46- 3, 2.5, 0, -2, and 1. So our minimum is -3, and then our maximum is, let's see, I should be careful, I shouldn't use this, this dash, it looks like a negative. So for our x values, our minimum is -3, and then our maximum is, looks like the highest value for our x values is 2.5.

1:09Fair enough. And now let's look at our y values. So on our y values, our minimum is, let's see, -1.5.

1:19- 1.5. And our maximum value goes to, let's see, is it 0? No, it's 1.2 right over here. 1.2. So I wanna set up my axes, so I capture all of, well, I wanna capture all of this range in both the x and y direction, so let's first think about the x. So if this is my x axis right over there, I'm going to wanna go to, I could go from -3 to, say, +3.

1:50So this is, so if this is 0 right over here, 0, then that's 1, 2 and 3, and then that would be -1,

2:05- 2 and -3. I'll definitely be able to plot those points and they won't all be scrunched up. And now if I think about my y-axis, I might want to go from, let's see, I could go from 2 to -2. I could even go from +1.5 to -1.5. It doesn't have to be the same on either end, but these are close enough and so might as well do that.

2:28So let me do that. So let me make my y-axis here, and this is y. And if I want, let me go from +1.5 to -1.5. So that is +.5. And notice, the scales aren't the same on the x and y direction. That's okay. So this is +1.5, sorry, +1.0. And then this right over here is +1.5.

2:54And then this would be -0.5, - 1, and then -1.5. And now I can plot these points. This first one, -3, -0.8,

3:07- 3, -0.8 would put us right over there. That's point F. I'll do a few more of these. I don't necessarily have to do all of them, but let's see, 2.5, 1.2. 2.5 and 1.2 would put point G right over there. And then if I have point H at 0, -1.5. 0, -1.5, that is point H, I might as well just keep going.

3:37I have point I here, -2, 0.6. - 2, 0.6, right over there, that is point I. And then last but not least, I have point J which is at 1, 0. 1, 0, right over there. And so notice, when I picked this minimum and maximum for our x and y-axes, I'm able to fit everything, it's not all scrunched up, I can easily see the data.

4:02Now, let's do the same exercise over here on the right. So same idea, if I think about x what's our min and our max? So our minimum x value is -25, looks like. Our maximum x value looks like it is 30. And then if I go to y, y, the minimum value is -12,

4:33- 12. And my maximum value is, it looks like it is 20. All right, now you might already appreciate, you wouldn't be able to even plot most of these points, if any of them, on these axes right over here. That's why the scale is important. And as we're going to see, the scale that I pick for these right set of points, if you use those, these on the left would be super scrunched up, so that's why it's good to look at the data that you're dealing with.

4:59So for my x, maybe I go from -30 to +30. Once again, it doesn't have to be the same, it doesn't have to be symmetric like that, but why not? So if I say that this is 0, and I go 10, 20 and 30, and then this is -10,

5:20- 20 and then this is -30. And then in the y direction, let's see, I could go from, if I wanna make it symmetric, I could go from -20 to 20 or let's go from -15 to 20. So -15, let me start right over here.

5:38- 15 to 20. So let's say that this is 5, 10, 15, 20, and then this is -5,

5:51- 10 and -15. This is my y-axis, and of course, this is my x-axis right over here. And so once again, let's plot some of these points. So -25, 18.

6:06- 25, 18 would put us right about there. That's point P. We could look at 15, -12. 15, -12, right about there. That's point Q. We could go to -10, 20.

6:26- 10, 20. So that is point R right over there. We could go to 30, -5. 30, -5, point S. And then last but not least, if we say 0, 8. Let me do it in a different color. If I say 0, 8. 0, 8 would put us right about there. That is point T. And so notice, I would've had trouble plotting these points on these axes.

6:56And if I plotted these points on this axis, it would've been all scrunched up right close, too close to make sense of the data to our origin.