# NL1 GRAPHING LINEAR EQUATIONS

This eighth grade mathematics lesson focuses on making linear formulas. The lesson was originally 46 minutes in duration; however due to the editing out of a video segment that was shown during the class, the footage in this version is 42 minutes. There are 24 students in the class.

TimeCaption
00:00:05But you did make it?
00:00:06No.
00:00:07Once again you forgot to? That's not too smart. Did you at least bring your books?
00:00:14Yes.
00:00:15Well, I'll make a note of it.
00:00:21There's a couple of assignments that I didn't get back yet.
00:00:23Which ones?
00:00:24The- two of the additional exercises: two B, three and four.
00:00:28I didn't even get to do any of the additional exercises, Miss.
00:00:31Because I had a catch-up test (inaudible) I didn't have any time left to do this.
00:00:33Yes. So you're at two now?
00:00:37Yes, two B.
00:00:39Are you going to catch up with that before the next class?
00:00:40Yes.
00:00:41Yes?
00:00:42I didn't do the additional exercise at all.
00:00:43Because?
00:00:45Because (inaudible). But I did do this.
00:00:50This one you did make?
00:00:51Yes.
00:00:52You too, Arnela?
00:00:53Eh-
00:00:54Did it work out?
00:00:55Well, except for the last one.
00:00:56Except for the last one.
00:00:59Very well, we are going to begin.
00:01:04Will you take your books and notebooks out in front of you and bags on the ground.
00:01:12Marian, will you also put your bag on the ground?
00:01:19And then you may open up your books and notebooks.
00:01:22We may?
00:01:23You may.
00:01:27We are, uh, first going to discuss two problems. Then we will watch a section of video on this chapter.
00:01:36And I understand from several students that not all of the additional exercises have been done by everyone,
00:01:41not to say that some haven't done them at all.
00:01:44So, this will then be-
00:01:45(inaudible)
00:01:46Sorry?
00:01:47Is that for Wednesday?
00:01:49Yes (inaudible).
00:01:50I think you-
00:01:51(inaudible)
00:01:52Yes, but not completely. Some people haven't finished that section completely.
00:01:56Uh, so we will just add that to the homework for next time. Um, I won't discuss it for now.
00:02:01But you can ask questions about it. Especially those people who had such difficulty with those, uh, uh, equations,
00:02:09for that we'll have to do some hard work during this class session, yes? We will start with problem 23.
00:02:10Take that one out in front of you. Twenty-three.
00:02:18I'm starting (inaudible).
00:02:21Charles! Very cozy how you chose to sit in the back like that.
00:02:25That way I can see better.
00:02:27Are you going to participate and would you sit up straight, though?
00:02:33Problem 23, a graph has been drawn there, Brian, and shown is a- well, you have to make an equation with it.
00:02:46And that is actually what we talked about the entire last class session,
00:02:50so I'm curious to know whether you succeeded in making this type of equation alongside a graph.
00:02:57I succeeded.
00:02:58You succeeded?
00:02:59Yes.
00:03:00Beautiful.
00:03:01Succeeded?
00:03:02I didn't.
00:03:04Succeeded even marvelously. Linda?
00:03:07No way.
00:03:08Make my day.
00:03:09Yes, because you skipped a class, right? Marion, did you succeed?
00:03:14Yes, a little bit.
00:03:15A little bit?
00:03:16Not exactly.
00:03:18Succeeded?
00:03:19No.
00:03:24(inaudible)
00:03:25Well, let's just have a look then. I am just going to write down some equations. Uh, your answers.
00:03:31Um, Simon, what did you get?
00:03:34Uh...
00:03:35Nothing.
00:03:39Oh, I don't have that one.
00:03:40You don't even have that one. Okay, Tonny? What is your answer? What's the equation?
00:03:46Twenty-three.
00:03:50Peter?
00:03:51Y times zero point five plus one equals X.
00:03:54Y times zero point five...
00:03:55Plus one-
00:03:56times zero point five, and then?
00:04:00Plus one.
00:04:01Plus one. And then?
00:04:04Equals X.
00:04:05Equals X.
00:04:10Sharone?
00:04:11Uh, Y is three plus one times X.
00:04:17Oh, now- now you lost me. One plus?
00:04:20A half,
00:04:21A half,
00:04:22Times X.
00:04:23Times X. Okay, Stefan?
00:04:28Y is a half times X plus one.
00:04:32Okay, Mina?
00:04:34I have that.
00:04:35You have that one too. Any more different answers? What do you notice about these last two equations?
00:04:41They are the same.
00:04:42The other way around.
00:04:43Yes, they are simply the same. It's fine if you first write the one down, or the half times X. So these are the same.
00:04:50Usually we take the bottom one, that is the way we have practiced it lately, first with the X and then the separate number in the end.
00:04:56But this one is also correct, that is allowed as well. And let's go to the top one.
00:05:04Is that one different or is it also the same? Maarten?
00:05:07The Y is reversed.
00:05:08The X and the Y are reversed. You have "equals X" and they have "equals Y". Only they started with that, yes?
00:05:18How do you know what letter, what letter is separate? What will the answer be? How can you see that in the diagram?
00:05:27The vertical line.
00:05:29That one is on the vertical axis, Peter. What you fill in is always located on the horizontal axis, that's the X and what is on the vertical axis-
00:05:37you always do that secondly like we saw yesterday. That is the outcome and that has to be placed at the end. Yes?
00:05:44Very well, so that is the equation. Uh, question B. Calculate the value of Y if X equals 10.
00:05:49All you need to do there is to fill in a 10 in the place of the X.
00:05:55Y equals- I will copy that one half, times 10 plus one. First do times, one half times 10 equals five. And next do five plus one, which equals six.
00:06:08And so the answer is Y equals six. Okay, we will go to problem 27.
00:06:18Problem 27 is actually similar to the one we did yesterday and that was tricky.
00:06:24It is the last problem in, uh, the section, so we should really take a look at that one.
00:06:28I want to ask while you're looking at this problem-
00:06:34For which of course you'll have several answers because you have checked which one belonged where, to which line,
00:06:39that you take one- when I call your name, you may select one- one equation and then you may explain to me why it belongs to that line.
00:06:48Who wants to do the first one? Any volunteers?
00:06:52(inaudible)
00:06:54Arnela, would you like to try one?
00:06:55Um...
00:06:56Of course you do, come on. We practiced them yesterday. No, you may choose the equation. Which of those four equations would you like to do?
00:07:05Let's do... um... A perhaps.
00:07:10A perhaps. Uh, A. The equation of A is four minus three X equals Y.
00:07:21Okay, try to explain to me which one of these four lines belongs to that.
00:07:27Uh, well, personally I thought it might be one.
00:07:29You thought one. Explain why.
00:07:32Well, because it, uh, well, I thought that those black lines crossed the vertical line at four.
00:07:44You thought that this intersecting point would be approximately at four. Yes?
00:07:50Okay, but why, uh, what if the four were over here? Is that also still possible?
00:08:00Who can explain a little bit more? This line is a descending line, can you also tell that from the equation?
00:08:07(inaudible) descending value.
00:08:09Yes.
00:08:10And the one the least was subtracted from, that's the number one.
00:08:15Okay. Which ones, uh, are descending? I will write all four of them down. Uh, we have this one.
00:08:22We have Y equals two-and-a-half X minus three. We have Y equals two-thirds X, and we have Y equals five minus three X.
00:08:35Mark, which of the four are descending? Descending lines?
00:08:40Um, A and D.
00:08:41A and D. A and D. How can you see that? Ricardo, how can you see if an equation belongs with a descending line?
00:08:51It runs like this.
00:08:52Yes, you can see it on the diagram. But how can you tell that from the equation?
00:08:56If it has a little minus mark.
00:08:57Yes, but where does the minus mark have to be?
00:08:59It has to be, um, it has to be, um, in front of the slope.
00:09:05In front of the slope, yes. Because I see three minuses here, and yet there are only three descending lines.
00:09:12Yes, the slope, that is the number by which you multiply so this one is descending,
00:09:19that one is not, that is just the starting number. And this one is descending. So, either this is one or that is one.
00:09:28Let's take a look at the starting number. Douwe? What is the difference in starting numbers between these descending lines?
00:09:36Are you still able to see that, or not?
00:09:37Not really.
00:09:38Not really.
00:09:48It's a bit light isn't it?
00:09:51Like this?
00:09:54It is also shown in your book, right?
00:09:58That may be easier. What is the starting number of A?
00:10:04Um, four.
00:10:06Four. What is the starting number of D?
00:10:09D?
00:10:10D. Dirk?
00:10:13(inaudible)
00:10:15No, that is not the starting number.
00:10:18Five. Here, the starting number is four and there the starting number is five. Oh, then this must be four and then that must belong to the five.
00:10:32Then this one will belong to one, and that one belongs to two.
00:10:41I still have two equations left. Which one belongs where? Um, Arnold?
00:10:49Uh, B is three and you add that (inaudible).
00:10:57Starting number is minus three. Well, this is the only one that has starting number below zero. So most likely minus three lies here.
00:11:05And this one has exactly zero as a starting number. How can I find that one in here? Niels? I don't see any zero here.
00:11:16No (inaudible).
00:11:22Charles? What is the deal with that?
00:11:26Uh, one.
00:11:27No, but I would like to have a word with you shortly, Charles.
00:11:30That's fine.
00:11:31Very well. Maarten?
00:11:33You don't have to write the zero down.
00:11:34Yes, it actually has plus zero behind it, but they didn't write that down.
00:11:39They just left the zero out, plus zero you can just leave that out.
00:11:42The starting number zero, and that is this line. Okay, uh, I'm noticing that for several people it hasn't quite sunk in.
00:11:50So I am just going to walk around shortly during the additional exercises, and I'll check how things are going and what you wrote down.
00:11:55There were several people who didn't have problem 23. I'll stop by and take a look at those, too. And, uh, then you need a little extra practice with those.
00:12:02Yes? Okay. We are just going to have a look at a little piece of video about this chapter.
00:12:09And while you're watching I want you to, uh, uh, try to remember from the video in which professions this subject- graphs, uh, relationships,
00:12:21something might even show up about a slope and a starting number,
00:12:25so in what professions you will come across that. I would like you to tell me those things afterwards.
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00:14:31Okay, here is where we stop.
00:14:36You have, um, come across the linear relationships within several things.
00:14:42Um, Casper, why don't you name one?
00:14:44In scuba diving.
00:14:45Excuse me?
00:14:46In scuba diving.
00:14:49In scuba diving, right. Have any of you ever dived?
00:14:53Yes? How was that? Fun?
00:14:57I always find the breathing so difficult under water, so eh, huh? But do you do it more often, or just once?
00:15:03In The Netherlands or uh, somewhere?
00:15:05In France.
00:15:06Well, well. And you, Ricardo?
00:15:08Well, soon I'm going to dive with my (inaudible) at a diving beach.
00:15:12Oh, yes. Exciting! Jolly. And what else did we come across?
00:15:16Cell phones.
00:15:17With cell phones, right, when you want to compare prices.
00:15:21Then you have a starting number, that is the starting amount that you pay for the subscription and how much per unit is added.
00:15:27The braking distance.
00:15:28Excuse me?
00:15:29The braking distance.
00:15:30The breaking distance. Was that linear?
00:15:31No.
00:15:33No, that was not linear, was it? The faster you drive, the more is added to braking distance. Yes, that was not a linear relationship.
00:15:41The skating.
00:15:42The skating. Yes, we looked at that.
00:15:44Alcohol checks.
00:15:45Alcohol checks. With alcohol it wasn't linear either, right? If you start drinking more, that won't be quite like in a linear graph, no.
00:15:55Very well, anyway we came across quite a lot of different things. Um, I am going to assign your homework and then you can get to work.
00:16:00I will just walk around, therefore raise your hand if you have any questions. That is for... tomorrow.
00:16:12Can you pass me a sheet?
00:16:17Fifth period...
00:16:25Do page 53 and page 54. And in case you didn't complete page 52 yet-
00:16:35That's an awful lot.
00:16:36Yes.
00:16:37Those are two pages, yes.
00:16:38Yes.
00:16:39Nothing out of the ordinary.
00:16:41Then you still have to add that page, right?
00:16:47I will be right with you.
00:16:57:00]
00:17:00Yes.
00:17:01Uh, tomorrow I will have a look at notebooks again, "by the way"...
00:17:04By the way...
00:17:05By the way... So be sure to have that taken care of. Just a minor warning. If not, then I'll have a neat surprise.
00:17:15Oh, we'd love a neat surprise.
00:17:17That is what I thought. Is your notebook in order? Oh, what a nice looking folder.
00:17:23I thought that you were- you were going to make an appointment with me yesterday?
00:17:26What?
00:17:27Yesterday you said "I'll swing by to make an appointment" because you would have your notebook, eh,
00:17:33with you, remember that? But you were gone at the end of class.
00:17:36A double appointment.
00:17:37Why don't you just remain seated for a moment at the end of class, okay?
00:17:39Yes.
00:17:45Yes, would you put that neatly into a folder? Yes? So we can check it.
00:17:52Fifty-two, 53, 54.
00:17:54Next time I want to check your notebook to see if everything is in there.
00:17:59Teacher, may I (inaudible)?
00:18:04How about just making it by yourself? How far are you?
00:18:07At 26.
00:18:08Sorry?
00:18:09Twenty-six.
00:18:10Then keep going with it.
00:18:16Let's see for a second those exercises from, uh- yes, the ones you did. Check those for a moment.
00:18:23And Charles, why where you not participating earlier?
00:18:27Yes, but seems to occur quite a lot these days. Your homework is not in order.
00:18:31No, I didn't understand it...
00:18:33I am not happy about that. Is one of your parents attending the upcoming Parents Night?
00:18:38Because I will have a talk about this. I have warned you so many times and now I want you to finally straighten up.
00:18:44Will it be done tomorrow?
00:18:45Yes.
00:18:46Yes?
00:18:47Yes, tomorrow it will be finished.
00:18:48Excellent, so for now you better get on top of it.
00:18:50Teacher?
00:18:51Yes?
00:18:52I would love to have my grade of my math paper.
00:18:55I will have a look. Yes? And you are not sure yet either?
00:19:00I don't understand problem 25.
00:19:04Twenty-five. In the graph you will see how the amount of water goes down in the boiler during showering.
00:19:11Write down a linear equation in which you can calculate how much- well...
00:19:16I don't understand that.
00:19:17So you should have? What do you need for a linear equation?
00:19:19Oh, uh, the starting number and the slope.
00:19:22Very good. What is the starting number? How do you find that in-
00:19:25Two hundred, that's-
00:19:26Well, very good! Okay, let's start with that. Well, you just had the letters the wrong way around.
00:19:32Yes.
00:19:33Which letter is the outcome?
00:19:38Uh... Y.
00:19:40Yes, that is always the Y. Which Y axis is here? Yes, very good. Yes, well, you have to pick a letter for that.
00:19:46Uh, just choose a letter. Uh, what letter shall we pick for that?
00:19:52The amount of water or something
00:19:53Well, multiply it by one letter, just one letter.
00:19:55H.
00:19:56H. Okay, "H equals" is a good way to start.
00:19:58H equals...
00:20:00The slope- or, uh, the starting number always comes all the way at the end.
00:20:05Yes.
00:20:07So you can go ahead and write that down already. Yes, it is a positive 200.
00:20:14Uh, I am under the impression that not everyone is working.
00:20:18I can't really see why, but... go ahead and get started, I will be by in a minute. Come on.
00:20:29So it is?
00:20:30Positive.
00:20:31Positive. So do you add it up or do you subtract it?
00:20:35Well, then write a little plus in front of it.
00:20:37Okay, now we need to do something with the other letter. What letter will we take for the other axis?
00:20:42No, this will be- this will become one equation.
00:20:45Oh-
00:20:46Just like you have made one equation here.
00:20:49Where do you have the other one?
00:20:50Yes, it looks kind of sloppy.
00:20:51Yes, that one you should write down a little more neatly because it's difficult to reconstruct this way.
00:20:58Let me see, X-
00:20:59Y equals- put that one up front. And then the number you multiplied with. That was zero point five times X, simply X.
00:21:11Something like this.
00:21:12Okay. Plus one, it says there. That is how this equation should be as well. You already have "H equals", that is the same as this.
00:21:20H equals, and then the slope-
00:21:22Here you have plus one and over here you have plus 200. Now you still have to-
00:21:24Insert the slope.
00:21:25Correct.
00:21:26That is, let me see, that is minus, that is minus one- oh, that is minus-
00:21:33It is minus anyhow, you've seen that correctly. Go ahead and start by writing the minus down, because it descends.
00:21:37And the slope is always when you go one step to the right. But that's kind of hard to see, how much one step is.
00:21:43Can you tell me what would happen if you went 10 steps to the right? How many steps do you have to go down, then?
00:21:50Uh, hang on, also, also 10.
00:21:53Let's just have a look. Go from 10 to the right, we will arrive at this point. Where are we?
00:21:59At 100. At the hu- like this at the 100 one- four steps?
00:22:09Do you have a pencil for me?
00:22:15Come on, start working.
00:22:21That's this point.
00:22:23Oh, that point.
00:22:24Here it lies at the 10, and here it lies at the?
00:22:28One hundred twenty-five.
00:22:30Okay, so if I go 10 steps to the right, then I have to go down 125. If I go 10, 10 steps to the right,
00:22:45I have to go down 125.
00:22:48But I would really like to know how that works with one step, with one step to the right.
00:22:57That has gotten how many times smaller?
00:22:58Ten.
00:22:59Divided by 10.
00:23:00One hundred twenty-five divided by 10 is twelve-and-a-half.
00:23:02Okay, and this is the vector number, or the slope.
00:23:07Oh...
00:23:08And that was a negative- and you still need to put a letter in front of the axis. Did you also have a question?
00:23:13Yes. I, um, I was sick yesterday so I don't have 12 through 19.
00:23:21Yes, okay. And did it work out?
00:23:24Well no, I still need to do that.
00:23:26Those ones you haven't done yet. Where exactly are you?
00:23:28Right now?
00:23:29At which problem are you now? Which problem did you complete?
00:23:33At 27.
00:23:35And this one you haven't done?
00:23:36Right, I skipped that one.
00:23:37That you cannot do. You can't just skip problems and then proceed with other problems.
00:23:42That is impossible, because then you don't understand those yet.
00:23:45Yes, a little bit, I do find it to be quite difficult.
00:23:47Yes, I can imagine. But at what problem did you end?
00:23:49At 12.
00:23:50At 12, so then continue with 13.
00:23:51And don't do the additional exercises for tomorrow, instead you just go as far as time allows you to.
00:23:57Yes.
00:23:58Preferably more than two pages, otherwise you will fall behind even more.
00:24:01Yes, okay.
00:24:02Start with this problem and then come and see me any time there's something you can't figure out, so that I can help you move on.
00:24:14I will make an appointment with you later because- yes, no, I think that you are working badly-
00:24:18Well, at least sit straight and get to work, please!
00:24:21Teacher, I have been checking the wrong chapter, I thought-
00:24:25Oh, that is smart.
00:24:26:00]
00:24:44May I briefly interrupt? I want the both of you to write down a clarification for yourselves at problem 27.
00:24:50Okay.
00:24:51So that you explain to yourself why that line is there, otherwise you will never find it back.
00:24:57Okay.
00:24:58Hm!
00:25:09Yes, I know because I came to- A has the starting number four. And-
00:25:16Shall I demonstrate it on squared paper? That way you can see it very clearly.
00:25:20Yes, because that one's lower, that other one.
00:25:23Look, have a look. I will put it on top of the squared paper. I have put squared paper underneath it.
00:25:32Are you able to see now...
00:25:40Can you now figure out for each line what the starting number is, what the vector- the slope is and what the equation is?
00:25:50Why don't you close problem 27 in your book and grab your notebook and write down the equations of these four lines.
00:26:01Equations?
00:26:02Uh huh.
00:26:05Okay, um-
00:26:07Y equals...
00:26:11Simon, I also have a nice little assignment for you.
00:26:13Y equals four-
00:26:15Oh yes.
00:26:16But I am busy correcting.
00:26:18But you had problem- but you didn't understand problem, uh, what was it again, 23? You weren't able to figure that one out either. Huh?
00:26:24(inaudible)
00:26:25You didn't have that one, right?
00:26:27Here I have drawn- Simon, four lines here.
00:26:31Right.
00:26:34Would you, without having your book open, be able to write down an equation of those four lines?
00:26:47Would you? Would you like to give that a try?
00:26:50Sure.
00:26:53Yes, maybe your neighbor would like to join as well.
00:26:54Yes, he does.
00:26:58Are you able to do this?
00:27:05Let's have a look.
00:27:06I will indicate clearly where the reddest points are.
00:27:09Let's see. The green one is not very legible.
00:27:12:00]
00:27:19Times three.
00:27:21You mean: times minus three.
00:27:23No, it's minus three times-
00:27:26Hello! Four minus three...
00:27:30No, I know that.
00:27:33In case more people are having difficulties in making the equations, you could close your book for a moment and try to do this one.
00:27:40You don't have to, but you may. It is good practice.
00:27:44We don't really understand it. I think.
00:27:46Well-
00:27:47I understood it, but now I don't understand it anymore.
00:27:48Well, you will not understand it until you can truly solve it. When you can really do it.
00:27:56Take a line...
00:27:58Okay, A. A, line one.
00:27:59Line one. What do you need to know before you can make an equation?
00:28:03The starting number and (inaudible) number.
00:28:05Go ahead and see if you can find the starting number and the slope.
00:28:08I have four and minus three.
00:28:10But how can you place that in the equation?
00:28:11Yes.
00:28:12How do you start your equation?
00:28:13Y.
00:28:14Well, why don't you write that down.
00:28:15That's what we have!
00:28:16Well great, then let's see what you have?
00:28:17I have Y is four.
00:28:19Y is four and this I can't read-
00:28:22Yes.
00:28:23It shows a hyphen.
00:28:24Yes, I had X, times X or so.
00:28:27Just four X. Minus three is?
00:28:29Yup, I also have that. Minus three is-
00:28:31What comes after that?
00:28:32Is X.
00:28:33No, but that is not possible.
00:28:34No, because you started with "Y equals"-
00:28:37Yes.
00:28:39Oh, okay
00:28:40Y equals four X minus- minus three-
00:28:42Minus three. I have that, too.
00:28:44Okay.
00:28:45And then what?
00:28:46Well, very good. Then do the red line.
00:28:47Oh, is this one finished already?
00:28:49S?:00]
00:28:52That is all there is to it! Because now you have the whole equation.
00:28:55Listen, you can check it by saying "I have the letter X, I have the letter Y, and I have a starting number as well as a slope".
00:29:02And then you are done.
00:29:03Okay.
00:29:04Okay, uh...
00:29:06Y equals. Y equals five.
00:29:08Isn't it three? We're going from line two-
00:29:13Arnold? Come on.
00:29:17Y equals five. Um...
00:29:24Times-
00:29:27Five times X minus- minus three.
00:29:31No, that is not possible because, since then you've got (inaudible).
00:29:34No, minus one, two, yes though, minus three.
00:29:38And then? Teacher, we got the second one too.
00:29:44Super. What- and what is it?
00:29:46Well, I am not saying anything-
00:29:47I got it, though.
00:29:48Yes?
00:29:49Y equals five times minus three- X minus three.
00:29:52Five X minus three. Yes, very well done. And now, what's the starting number?
00:29:57Five.
00:29:58Okay, what is the vector number- the slope?
00:30:01Minus three.
00:30:02Okay, you should always begin with?
00:30:05Uh, Y equals five.
00:30:09Yes, but why five?
00:30:11Well, because that is the starting number.
00:30:12We always put that at the end. You've also put it at the end over here.
00:30:15No, because four is the starting number.
00:30:17Ooh. Yes, it is the wrong way around.
00:30:21But you just said that it was correct.
00:30:23Yes, that was silly of me, I didn't see that. No, I was looking upside down and therefore didn't see it well.
00:30:29No, the- the- the starting number is always the independent variable that is written at the end.
00:30:33This is what I drew, how I-
00:30:34Yes, that four is added in every step.
00:30:37So then this is also, this is also the wrong way around. That la- two.
00:30:40Uh, four X minus three. Yes, it is the wrong way around.
00:30:45Oh, and the last one too?
00:30:46And the last one-
00:30:48Y equals minus three.
00:30:49Yes. Right.
00:30:50Uh, times-
00:30:51Times five. No, no, no: times X minus five.
00:30:57Why don't you begin by writing down "Y equals".
00:30:59Y equals minus three. Doesn't it?
00:31:03Yes.
00:31:04X- or no, minus four, four, X four.
00:31:12It is a positive four. It is on the upper side and a positive four is a plus four.
00:31:18If the starting number is negative then it is a negative number and then it is minus four or minus three or whatever...
00:31:26But when it's on the upper side than it is plus.
00:31:28Yes, but you don't have to write the plus down?
00:31:30You do write it down because it has to be added on to it. So what do you get? Write it down again, write it down again.
00:31:36This number one?
00:31:37Yes?
00:31:39Y is-
00:31:40Yes?
00:31:41Minus three-
00:31:42Yes?
00:31:43X, um, minus four?
00:31:48It is located on the upper side-
00:31:49Oh no, it is four, four!
00:31:50And, something has to be inserted.
00:31:52Yes, but that's what I can't figure out.
00:31:54Is it a positive four or a negative four?
00:31:56Oh, plus four.
00:31:57X plus four.
00:31:58Yes!
00:31:59But in the book it is shown differently.
00:32:00No. Just write it down this way for now. This way is correct.
00:32:04Three X, and I put this here.
00:32:06Correct!
00:32:07Okay.
00:32:08All right. Now the next one, now the red one.
00:32:11Is it working or not?
00:32:14Yes, with the red one.
00:32:15You got the red one? Tell me about it.
00:32:17That is the (inaudible).
00:32:21No.
00:32:24No, because that's the slope!
00:32:27Look, you have the slope correct and the starting number correct except the starting number is always written at the end.
00:32:36This is how that's written.
00:32:38Y equals, and then over here you put the slope, and that you multiply with X. And then over here is the-
00:32:52Starting number.
00:32:53Starting number.
00:32:58Yes? And you have- this is the slope. That goes over here-
00:33:02That has to be the other way around.
00:33:03Right. Well, yes, but that is as different as day and night. It is a totally different equation.
00:33:06Yeah.
00:33:09Why don't you write it down correctly.
00:33:11(inaudible)
00:33:12You better start over again otherwise it- it'll get so messy that you will never be able to find it back.
00:33:28Shh. Keep going, I will be right over. I'll be right over.
00:33:36Yes, and over here you still need to add a- a symbol in between here. Is it a positive five or a negative five?
00:33:43Uh, negative.
00:33:44Let's see, where is the diagram?
00:33:46Right there.
00:33:47This red line. Here is the starting number. Is it a positive or a negative number?
00:33:52A negative number because it goes down.
00:33:57Positive.
00:33:58It is positive because it lays above the axis. If this were the intersection then it would have been negative.
00:34:01This is positive. So it is a positive five. What you have is a negative five. Now go ahead and make the- you want to have a plus here.
00:34:13Don't just simply remove it because then there's nothing there anymore. Plus five, it needs to be added on.
00:34:18Now do the black one.
00:34:20Teacher, you are not explaining it correctly because the book says something else.
00:34:25Yes, well, the book has a different sequence but it is correct, though. Look what- which one did you have? This one.
00:34:31Y equals minus three X, that's what you guys have, plus four.
00:34:36Except they put the four in the front because in the book they have shown it in a different sequence. The sequence doesn't matter.
00:34:42Yours is correct. And I think it is much more- Arnela, listen for a second, please.
00:34:47I think it would be much easier for you guys if you always used the same sequence.
00:34:51What the book is trying to do is make it more complicated by changing the sequence as well.
00:34:55But if you keep using the same sequence at all times, then you make thing a lot easier for yourself.
00:35:01This is exactly the same thing as is shown over there, except in a different sequence.
00:35:05Okay.
00:35:06Yes?
00:35:07So we should do it in this manner.
00:35:08Yes, that is what I would do, yes. That gives you some grip on it.
00:35:11Begin with the starting number?
00:35:12What?
00:35:15You always start with the slope. And then- write it down at least. Write it with red or some color.
00:35:22Yes, there it is already! Okay, yes.
00:35:26So we'll put this one down- that is also allowed, we are going to put that at the end, but look: the slope multiplied by A.
00:35:31Yes, and then what?
00:35:32The slope is separate. If you find it easier you may also begin with the starting number,
00:35:38but you did: starting number times X.
00:35:42But-
00:35:43Oh, yes, that's at the end.
00:35:44Correct. So generally the sequence is irrelevant. However please choose a sequence for yourself.
00:35:51If you choose a different sequence every time, you will get confused.
00:35:54Write down for yourself how you are now going to do it in the additional exercises.
00:35:59What sequence will you take each time?
00:36:02And it doesn't matter to me, you can choose it yourself. But you do have to choose one.
00:36:06And maybe it would be smart to choose one that is the same for both of you.
00:36:09Then you can help each other out every time.
00:36:11Or spy.
00:36:12For example, yes.
00:36:15The slope...
00:36:17And then the starting number.
00:36:19Eh, two, four, six, seven-
00:36:32And then?
00:36:34What do you mean: And then?
00:36:36Starting number!
00:36:37Yes. But didn't you always have to (inaudible).
00:36:40Yes?
00:36:42I don't quite get four.
00:36:49Whether this is linear? We have looked at two ways to find that out. The first way was?
00:36:55A table.
00:36:56Yes. You may do that. You could say I am going to make a table for each of them and then I'll check-
00:37:03How can you tell by looking at the table whether they are linear?
00:37:06When they're all equal steps.
00:37:08Correct, you may do that.
00:37:09And the other way we observed yesterday, well, we said to each other that we could also check which ones are not linear.
00:37:16No, that is two.
00:37:17Do you remember that series we just wrote down?
00:37:20You have to square it.
00:37:22Yes, squared. You need to memorize that. You may also do that. For instance you could say, well, B is not linear because it contains a number that's squared.
00:37:32You are also allowed to write that down. But if you say you find those tables easier because that way you don't have to memorize them, that is just as well.
00:37:36With that- with that letter that's not minus either. is it?
00:37:38Very true, that is not linear either, very good.
00:37:40C is not linear either, then.
00:37:41C is not linear either, no.
00:37:43And the other two, if you- if you have a good look, you can recognize it because you may see something that looks like a starting number and a slope.
00:37:51Hers is not correct, of course.
00:37:52Then you already have an idea as to which ones they are. But then you still need to explain it.
00:37:57Either you use this method where it shows a number squared which tells you it's not,
00:38:01or you do it with a table and you say that each time equal amounts are added, so therefore it is.
00:38:04Okay.
00:38:05Yes?
00:38:06Y is: minus two-and-a-half X- minus two-and-a-half X and the starting number is?
00:38:24Do you have the black one already? Yes?
00:38:31Well, let's see. Y equals- so far so good.
00:38:35The starting number is four.
00:38:36Let's see about that. From that- what line did we have here?
00:38:39The black one.
00:38:40The black one. The starting number is four. That is correct. Very good, and now the slope.
00:38:46I thought it was minus one-third.
00:38:47That's kind of hard to see because here because it doesn't have any squares underneath.
00:38:51But over there you can see it, right. If you go one step to the right then you have to go three steps down to get back on the line.
00:38:58Well, down below it is negative- they run parallel to one another so they must have the same slope,
00:39:03the same direction, so their slope is the same.
00:39:06So that is also negative three, yes? Okay. One is kind of difficult so I would skip that one for now if I were you.
00:39:19Um, I think you are able to do the blue one.
00:39:28Shall I, um, with the blue one I will- let's see, is that right? Or do we have more here? Um,
00:39:40Well, this one is also not that easy after all.
00:39:41Just go ahead with the additional exercises because you will come across them here again. Yes?
00:39:46All right.
00:39:50Draw it with pencil and a triangular protractor.
00:39:53Teacher, do I have to- so far I have as starting number (inaudible).
00:39:57No. How do you always find the starting number?
00:40:01Um, where it, where it intersects.
00:40:03What line does it have to cut, and it's not intersecting, it is cutting?
00:40:06Oh, the, the...
00:40:09Yes, yes!
00:40:10One, the one.
00:40:11One. Very good, yes.
00:40:13And then the slope is two.
00:40:17If you go one step to the right-
00:40:20Yes well, aren't you, aren't you supposed to go down like that?
00:40:22To the right, always one step to the right, what are you supposed to do to get back onto the line?
00:40:31So over here I am going to go one to the right. What should I do to end up on to the black line again?
00:40:37One half, for example?
00:40:38One half, very good. So upwards is always positive, yes?