Learn Graphing, Coordinate Plane, Points, Lines, X-Axis, Y-Axis & Ordered Pairs - [5-7-1] - By Math and Science
Transcript
| 00:00 | Hello . Welcome back . The title of this lesson | |
| 00:02 | is called graphing ordered pairs . This is part one | |
| 00:05 | . I'm actually really excited to teach this because here | |
| 00:08 | we begin to start the process of learning how to | |
| 00:10 | graph graph points in a what we call a coordinate | |
| 00:15 | plane . Not lots of big words . It looks | |
| 00:17 | complicated but I promised by the end of this lesson | |
| 00:19 | you will understand what an ordered pair is . You'll | |
| 00:22 | understand how to plot or graph an ordered pair , | |
| 00:25 | how to connect the dots in the X . Y | |
| 00:28 | . Or the coordinate plain . And also to understand | |
| 00:30 | why we care about graphing anyway . Why do we | |
| 00:33 | spend so much time on graphing ? That's the other | |
| 00:35 | thing we're going to learn here . So for our | |
| 00:37 | first problem I think it's just gonna be easier to | |
| 00:39 | jump right into our first problem . So here we | |
| 00:42 | have a bunch of points . You see we have | |
| 00:44 | an ex uh we have a table here . We | |
| 00:46 | have an X . Column with numbers and we have | |
| 00:49 | a Y column that also has numbers . Now . | |
| 00:51 | The way you need to read this aside from the | |
| 00:54 | point is that over here we have what we call | |
| 00:56 | an xy plane or you might also see it called | |
| 00:59 | a coordinate plane , right . The thing I want | |
| 01:01 | to call to your attention here is that we have | |
| 01:03 | numbers in this direction along what we call this line | |
| 01:07 | or this axis . The horizontal axis is what we | |
| 01:10 | always call the X axis . So I'll put X | |
| 01:13 | right there and then the Y axis of the vertical | |
| 01:16 | axis here . This vertical line here , we call | |
| 01:18 | it the Y axis . So I'll put like a | |
| 01:19 | Y right there . So if you see somebody telling | |
| 01:22 | you this is the X axis . Uh This is | |
| 01:25 | the Y axis . You automatically know the X axis | |
| 01:27 | is always horizontal like this and the Y axis is | |
| 01:30 | always vertical . Now , if you only have the | |
| 01:33 | X axis , you would just be plotting numbers right | |
| 01:36 | here along this line . If you only have the | |
| 01:39 | y axis , you would only be plotting numbers along | |
| 01:41 | the Y line like this . But we have X | |
| 01:44 | and Y together . So because we have X going | |
| 01:46 | this way and why going this way ? When we | |
| 01:49 | put them together , we have what we call an | |
| 01:50 | xy plane . A plane is a flat thing , | |
| 01:53 | a flat surface . So when you see something called | |
| 01:56 | a coordinate plane or an xy plane or sometimes you | |
| 02:00 | see it called a Cartesian plane . That's another story | |
| 02:03 | why it's called that it goes into the history of | |
| 02:05 | who invented it . Then all of those things are | |
| 02:08 | referring to the same thing . Now here what we | |
| 02:11 | want to do is take these numbers and represent them | |
| 02:13 | on here , plot them on there and understand what | |
| 02:15 | they mean . Here we have an X . Column | |
| 02:17 | and a Y column . Now the way you read | |
| 02:19 | it is these numbers go together as a pair . | |
| 02:22 | The xy pair . These numbers go together as a | |
| 02:25 | pair . These numbers go together as a pair , | |
| 02:27 | as a pair , as a pair . The X | |
| 02:29 | and the Y . They're joined together as a pair | |
| 02:31 | there . Like partners . You can't really separate the | |
| 02:34 | X . And the Y values when we plot them | |
| 02:36 | . The whole point of it is that they go | |
| 02:38 | together in pairs . All right . So we look | |
| 02:41 | and cover up the rest of this table . The | |
| 02:43 | rest of this table means nothing . We're only going | |
| 02:45 | to look at this pair . We have X . | |
| 02:47 | Is equal to one and why is equal to three | |
| 02:50 | ? So in order to represent that point on the | |
| 02:52 | plane , we go in the X direction he down | |
| 02:55 | here only one unit over that means we stop right | |
| 02:58 | here because this is X is equal to one , | |
| 03:00 | so X is equal to one is right there . | |
| 03:03 | But why is equal to three ? Notice this is | |
| 03:06 | the Y direction . So we go over one . | |
| 03:08 | Which is this number and then we go up 123 | |
| 03:10 | C . It's right here and the intersection of these | |
| 03:13 | points uh those lines there , that's where we put | |
| 03:16 | a 0.1 , comma three . So we'll put a | |
| 03:18 | big fat dot right there . So what we have | |
| 03:21 | represented is that this .13 when X is equal to | |
| 03:26 | one and why is equal to three is represented by | |
| 03:28 | this dot on the coordinate plain . Now , I'm | |
| 03:32 | gonna take a second to jump down here and tell | |
| 03:34 | you that these , I have this in the table | |
| 03:36 | here . But what we often see in math is | |
| 03:38 | the points represented as a pair in parentheses . X | |
| 03:42 | comma Y . It's the same thing as this table | |
| 03:45 | . This first point in the table one and three | |
| 03:48 | would be represented as one comma three . So if | |
| 03:51 | you ever see a 0.1 comma three , you know | |
| 03:54 | that the first number is always X . And the | |
| 03:56 | second number is always Y . So when you see | |
| 03:59 | pairs of numbers in parentheses , the first number is | |
| 04:02 | X . The second number is why ? So you | |
| 04:04 | go to X is equal to one , Remember X | |
| 04:06 | is this direction and why is equal to 3123 And | |
| 04:10 | that places where you put the dot . Alright , | |
| 04:13 | next point we're gonna ignore everything above and below . | |
| 04:16 | We're only going to look at 35 So we know | |
| 04:19 | that X is equal to three . So we look | |
| 04:21 | in the X direction 123 that's X . Is equal | |
| 04:24 | to three and why is equal to five ? We | |
| 04:26 | go up 12345 noticed we went to y is equal | |
| 04:30 | to five . X is equal to three . And | |
| 04:32 | we put a dot at this intersection point right here | |
| 04:37 | . If we were going to write this in parentheses | |
| 04:39 | , we would call it three comma five and we | |
| 04:41 | already know X is equal to three and y is | |
| 04:44 | equal to five . Is that's how it's always written | |
| 04:46 | X comma Y . All right , next we have | |
| 04:50 | seven common nine . We know that X is equal | |
| 04:52 | to seven and Y is equal to nine . So | |
| 04:55 | X is equal to you . Just go to seven | |
| 04:57 | right there and why is equal to nine ? So | |
| 05:00 | we go up from here all the way up to | |
| 05:02 | nine . Notice that y is equal to nine . | |
| 05:05 | It's the intersection of these places right here . So | |
| 05:08 | seven common nine means that we put a dot at | |
| 05:11 | this point right here . All right , next we | |
| 05:15 | have two comma four , so X is equal to | |
| 05:18 | two . That's always the first and y is equal | |
| 05:20 | to 1234 right there , which is a dot right | |
| 05:25 | there . And then our last point is five comma | |
| 05:28 | seven , X is equal to 512345 and y is | |
| 05:32 | equal to 71234567 noticed that that's the seven and that's | |
| 05:37 | X is equal to five . So that final dot | |
| 05:40 | goes right here . So we have all the dots | |
| 05:43 | on the board and if we wanted to write more | |
| 05:45 | of these points , seven , uh X is equal | |
| 05:48 | to seven and y is equal to nine would be | |
| 05:50 | seven comma nine and then X is equal to two | |
| 05:53 | , Y is equal to four will be two comma | |
| 05:55 | four and then X is equal to five and y | |
| 05:58 | is equal to seven will be five comma seven . | |
| 06:02 | So you can put it in a table form or | |
| 06:04 | you can just write the points down the first numbers | |
| 06:06 | . Always X . The second number is always y | |
| 06:09 | . Now in this case , what does this look | |
| 06:10 | like ? This is a straight line of points . | |
| 06:13 | That's kind of nice . We're really when you look | |
| 06:15 | at it it's not going to be perfect . I'm | |
| 06:17 | not gonna be able to draw a straight a perfect | |
| 06:19 | line but I want to try to at least draw | |
| 06:22 | and connect these dots . So it's kind of like | |
| 06:24 | , you know back when you were younger and used | |
| 06:26 | to play connect the dots , you get to draw | |
| 06:28 | lines and connect the dots . All right , So | |
| 06:30 | that is our line and you can as we go | |
| 06:33 | through math , you will find that you can make | |
| 06:36 | all kinds of shapes on on these planes like this | |
| 06:39 | . We are always very interested in lines because in | |
| 06:43 | real life lines represent lots of things in real life | |
| 06:47 | . But we also have other shapes that will learn | |
| 06:49 | about later . You'll see even in this lesson here | |
| 06:52 | , we'll have other shapes that happened when we connect | |
| 06:55 | the dots . Now , I want to spend a | |
| 06:57 | minute to uh to to to uh talk about what | |
| 07:02 | this could actually mean . Why do we connect the | |
| 07:04 | dots ? Why do we need to do this ? | |
| 07:06 | Why are we plotting things ? So , I want | |
| 07:08 | to anchor it in your mind with a real example | |
| 07:10 | . Let's say we can just we can make up | |
| 07:14 | anything we want . So , let's say that X | |
| 07:16 | . Here really represents time in seconds . So , | |
| 07:21 | this is let's say I start to watch then , | |
| 07:23 | then this is one second , two seconds three seconds | |
| 07:26 | four seconds five seconds 67 So time is represented down | |
| 07:30 | here on the X direction . You could call it | |
| 07:33 | T instead of X if you want . And let's | |
| 07:36 | just say for this example that why is representing the | |
| 07:39 | temperature in this room ? Okay . The temperature in | |
| 07:42 | this room . So I know the numbers are a | |
| 07:44 | little bit weird . But let's say that I start | |
| 07:46 | my watch at one second after I start my watch | |
| 07:49 | , the temperature is three degrees . But then at | |
| 07:51 | two seconds the temperature is four degrees . And then | |
| 07:55 | at three seconds the temperature is five degrees . And | |
| 07:58 | then when I skip down to 5°, , the temperature | |
| 08:01 | was 7°. . And then at seven seconds the temperature | |
| 08:04 | was nine degrees . What does this graph represent then | |
| 08:07 | ? What it's representing is a room that is warming | |
| 08:11 | up . That's what it's representing . We start the | |
| 08:13 | clock one second , two seconds , three seconds , | |
| 08:16 | four seconds . Four seconds would be about here . | |
| 08:18 | Five seconds is here and so on and that every | |
| 08:21 | second the temperature is going up by the same amount | |
| 08:24 | . That is an example of what this graph could | |
| 08:27 | represent . We can represent grass for lots of things | |
| 08:29 | . But the reason we actually use graphs is because | |
| 08:33 | we can visually see if we just put look at | |
| 08:35 | the numbers . It's hard to see what's happening . | |
| 08:37 | Like can you tell me what's going on here ? | |
| 08:39 | It's very hard to look at this and know what's | |
| 08:41 | happening . But when I look at a picture , | |
| 08:42 | I know immediately the temperature is increasing and not only | |
| 08:46 | is it increasing its going up the same amount every | |
| 08:49 | single second . That's why we use graphs . So | |
| 08:52 | , we can visualize things . All right . Uh | |
| 08:56 | And one more thing I'll say if you want to | |
| 08:58 | you don't have to . You can label the points | |
| 09:00 | on the graph . I mean we didn't do it | |
| 09:01 | here , but this is one comma three . That | |
| 09:03 | was this point . So we could put a parentheses | |
| 09:05 | one comma three for this point here . And we | |
| 09:09 | could label each one if we wanted to . You | |
| 09:11 | know , of course have to . All right . | |
| 09:13 | Let's take a look at the next set of numbers | |
| 09:15 | here . Here , we have another table . Uh | |
| 09:19 | and we have another blank graph . So , let's | |
| 09:21 | go ahead and uh plot these points and see what | |
| 09:24 | kind of shape this one makes . Alright to come | |
| 09:28 | a three . That means X is equal to two | |
| 09:30 | . Why is equal to three ? So X is | |
| 09:31 | equal to two . Goes this way . Remember this | |
| 09:34 | is the X direction and then appear is always the | |
| 09:37 | Y direction , so X is equal to two . | |
| 09:39 | Why is equal to 123 ? Which means there's got | |
| 09:42 | to be a dot right here . And don't forget | |
| 09:44 | , I'm not gonna do this for every problem . | |
| 09:46 | But if you wanted to write this as a coordinate | |
| 09:48 | point , you would say two comma three . This | |
| 09:51 | always means the first number is X is equal to | |
| 09:53 | two and then the second number Y is equal to | |
| 09:55 | three . Alright , next 0.8 comma nine , that | |
| 09:59 | means X is eight , Ny is nine , so | |
| 10:01 | let's go over to X is equal to eight and | |
| 10:04 | Y is equal to you can see right there . | |
| 10:06 | Nine , Y is equal to nine . X is | |
| 10:08 | equal to eight and we put a dot right there | |
| 10:12 | . Next 0.4 comma five , you could write that | |
| 10:15 | down as four comma five . That means X is | |
| 10:18 | four , Y is five , X is four is | |
| 10:21 | right here . Why is 12345 ? Which means a | |
| 10:26 | point would be right there . Next six comma seven | |
| 10:29 | , X is equal to 6123456 and y is equal | |
| 10:33 | to 71234567 Notice that why is equal to seven right | |
| 10:38 | there ? When X is equal to six ? Final | |
| 10:41 | 0.1 comma two . That means X is one . | |
| 10:45 | You can write it like one comma two if you | |
| 10:48 | like this one comma two is X is one , | |
| 10:50 | Y is too . And that means that at this | |
| 10:53 | point is right here . So again , I won't | |
| 10:57 | do it for every single problem . But let's try | |
| 10:59 | to draw and see what this actually looks like . | |
| 11:03 | If I line it up , it's not going to | |
| 11:05 | be exact is not going to be perfect . That's | |
| 11:06 | okay . We don't care about exactly . Just care | |
| 11:08 | about trying to understand what's happening . This is a | |
| 11:11 | straight line also that goes all through those points . | |
| 11:15 | So here again , we have points plotted and they | |
| 11:18 | make a slanted line , just like in the first | |
| 11:21 | example we can actually compare them and we can see | |
| 11:23 | the shape of that line looks more or less the | |
| 11:25 | same , but it's not exactly in the same location | |
| 11:28 | . Uh this line is maybe shifted up a little | |
| 11:30 | bit . This line is in a different position , | |
| 11:31 | but the slant of the line we call it , | |
| 11:33 | the slope of the line is basically the same . | |
| 11:36 | What could this represent ? Of course it could be | |
| 11:38 | temperature time here in temperature , but it could also | |
| 11:41 | represent something else . Let's say , just just just | |
| 11:44 | making this up , let's say I had a rod | |
| 11:47 | like this and this distance here , this this these | |
| 11:50 | numbers along X . Could be the distance along the | |
| 11:53 | rod . So literally this direction here is like a | |
| 11:56 | rod right here . And then what am I plotting | |
| 11:59 | down here ? I could be putting rocks on this | |
| 12:01 | rod . And the number here is telling me how | |
| 12:04 | many rocks I have at each position . So at | |
| 12:07 | one centimeter over I might have to rocks piled here | |
| 12:10 | at two centimeters over . I might have three rocks | |
| 12:13 | piled at at four centimeters . I might have five | |
| 12:16 | rocks piled . You see the pattern here ? At | |
| 12:18 | seven centimetres down over here , I might have or | |
| 12:21 | six centimetres . I might have seven rocks piled . | |
| 12:24 | So what it allows you to do , depending on | |
| 12:26 | what you're talking about is I can look at a | |
| 12:28 | picture and I can see , oh , I have | |
| 12:30 | fewer rocks here at the end of the rod and | |
| 12:33 | more rocks over here , near the other end of | |
| 12:36 | the rod . And the amount of rocks along the | |
| 12:38 | rod is going up up up up up at the | |
| 12:41 | same number of rocks , uh , as I go | |
| 12:44 | along . In other words , it's going up at | |
| 12:45 | the same amount as I go down the rod . | |
| 12:49 | All right now , let's change it up a little | |
| 12:51 | bit and do something different than a line . This | |
| 12:54 | one's gonna be really interesting . So pay attention to | |
| 12:56 | this one here , we have points of course , | |
| 12:59 | two , comma seven is our first point , so | |
| 13:01 | X is equal to two and y is equal to | |
| 13:04 | seven . If you wanted to write that as a | |
| 13:05 | point with the parentheses would be two comma seven . | |
| 13:08 | You write that as X is to y is seven | |
| 13:10 | . So again , the X direction is here and | |
| 13:13 | the Y direction is always up and down , X | |
| 13:16 | is equal to two . Y is equal to 1234567 | |
| 13:20 | means there has to be a dot right here . | |
| 13:23 | Next 0.3 comma three means X is three . And | |
| 13:27 | why is also three ? That means there has to | |
| 13:29 | be a dot right there . Next 0.5 comma zero | |
| 13:32 | , Xs five which is here . And why is | |
| 13:35 | zero ? That means there's actually a point way down | |
| 13:37 | here . Why here is zero way over here . | |
| 13:40 | So when I go to excess five , Y is | |
| 13:42 | zero . It doesn't go up at all . Because | |
| 13:43 | Y is zero down here . Seven comma three . | |
| 13:47 | You could represent . That is seven comma three . | |
| 13:49 | In the parentheses , X is seven , Y is | |
| 13:52 | three , X . Seven , Y is 123 means | |
| 13:56 | there's got to be a point like this . 8:07 | |
| 13:59 | X eight Eggs on his way over here . And | |
| 14:03 | why is 712-34567 means there has to be something here | |
| 14:09 | . Now . This one's really interesting , right ? | |
| 14:10 | Because this doesn't form a line . I mean you | |
| 14:13 | can try all you want but it doesn't form a | |
| 14:15 | line through all these points . In fact , if | |
| 14:17 | I go through these two points like this , it | |
| 14:19 | doesn't even hit this one . If I go through | |
| 14:22 | these two points like this , it still doesn't hit | |
| 14:24 | this one , there's no way to even catch these | |
| 14:26 | three points along a straight line . So this does | |
| 14:29 | not formalized . So you might say , what kind | |
| 14:31 | of shape is this ? Uh Sometimes when you draw | |
| 14:34 | grass you just have to draw the best curved line | |
| 14:37 | you can through it . Now , this is not | |
| 14:38 | going to be exact . Um But you can this | |
| 14:41 | line might be something like this . It might go | |
| 14:43 | through here , might go through here , hook and | |
| 14:46 | curve down and then go up something like this . | |
| 14:50 | Now , of course , I went up past the | |
| 14:52 | points there , you can put little arrows kind of | |
| 14:55 | pretending that the graph goes up beyond these points that | |
| 14:57 | I've plotted . But really , I guess with the | |
| 14:59 | data I have , it stops at these points there | |
| 15:03 | . Now , this is an interesting shape that we | |
| 15:05 | run into all the time in math . You'll see | |
| 15:08 | as you learn more and more , you'll you'll learn | |
| 15:10 | about these shapes . Uh more and more as we | |
| 15:12 | go along . But what could it represent ? Okay | |
| 15:15 | , what can it represent ? Let's go back to | |
| 15:18 | our rod example , let's say that the X direction | |
| 15:22 | is telling me how far from the end of the | |
| 15:24 | rod I am . So here's one centimeter two centimeters | |
| 15:27 | three centimeters four or 56 All the way to 10 | |
| 15:30 | centimeters . Right ? And then this direction here is | |
| 15:33 | telling me the temperature of the rod , Right ? | |
| 15:36 | So let's say that over here , near the end | |
| 15:39 | of the rod , at two centimeters , it's really | |
| 15:41 | high temperature seven degrees . But then as I go | |
| 15:44 | to the right , the temperature is dropping . Then | |
| 15:47 | the temperature drops to let's say zero . And then | |
| 15:50 | as I go past this point , when I get | |
| 15:52 | here at seven centimetres , temperature goes up again , | |
| 15:55 | and then the temperature goes up again . How could | |
| 15:57 | that be ? I mean , just an example of | |
| 15:59 | that would be , what if I had an ice | |
| 16:01 | cube if I put an ice cube right on the | |
| 16:03 | center of the rod right here ? Well , that | |
| 16:05 | would mean it's cold right in the middle . So | |
| 16:07 | the temperature is low . But as I go just | |
| 16:09 | to the left and to the right of the ice | |
| 16:11 | cube , it's a little bit warmer . And then | |
| 16:13 | as I get farther away , it's even warmer down | |
| 16:16 | here . So this could represent in distance this direction | |
| 16:20 | . And then this uh this uh Y direction is | |
| 16:23 | telling me the temperature which is going down to an | |
| 16:25 | ice cube and then going up again as I go | |
| 16:28 | again away from an ice cube . So I'd like | |
| 16:31 | to do is take these down and do three more | |
| 16:33 | to give you a little more practice . All right | |
| 16:36 | , here's our next problem . This one is also | |
| 16:37 | a really cool shape . Let's take a look at | |
| 16:39 | the 1st 10.0 for X and zero . For why | |
| 16:42 | ? If you wanted to write that in terms of | |
| 16:44 | a parentheses form that you see a lot . You're | |
| 16:46 | right . It is zero comma zero . That means | |
| 16:48 | X zero and y is zero . Well , if | |
| 16:51 | the again , don't forget , this is the X | |
| 16:52 | direction and this is the Y direction . If X | |
| 16:55 | zero , that means I'm right here , I don't | |
| 16:57 | go any direction over here . And if Y is | |
| 17:00 | zero , I don't go any direction up . So | |
| 17:02 | zero comma zero is right in the corner down here | |
| 17:05 | . We call it the origin zero comma zero is | |
| 17:09 | the Origin . It's the the lowest or the smallest | |
| 17:11 | point of the coordinate system where X and Y are | |
| 17:14 | both zero . Do you have a point at the | |
| 17:16 | origin now you have four comma one . You would | |
| 17:19 | write that as four comma one . Xs four . | |
| 17:22 | Why is one if X is four , that's four | |
| 17:25 | for X right here . And why would be one | |
| 17:27 | ? Why would be going up only one ? Which | |
| 17:29 | means there will be a point right there . Next | |
| 17:33 | seven comma 37 for X and Y for 3123 means | |
| 17:38 | there's a point right here . Next nine comma 69 | |
| 17:43 | for X and six for Why ? 123456 for why | |
| 17:47 | means it would be right here And then 10 comma | |
| 17:50 | 10 . We have 10 over here for X and | |
| 17:53 | 10 over here For why ? Which means there will | |
| 17:55 | be a point right here . Now again you have | |
| 17:58 | the same kind of problem as the last example . | |
| 18:00 | There's really no way to draw a line . I | |
| 18:02 | mean you can kind of draw a line this way | |
| 18:04 | , you kind of do something like this , but | |
| 18:06 | there's no way to capture all of these points on | |
| 18:08 | the line . So it's it's not alive . Let's | |
| 18:11 | draw our best shape that we can through here again | |
| 18:14 | . You just try to connect it with a smooth | |
| 18:16 | curve and my curve is not going to be perfect | |
| 18:18 | . So please forgive me . But let's just try | |
| 18:20 | to go up at this point . We're at this | |
| 18:23 | point at this point . And at this point that's | |
| 18:26 | not too bad . It's a little lumpy , but | |
| 18:28 | you get the idea now , what would something or | |
| 18:31 | what could something like this represent ? Let's say again | |
| 18:34 | that we had a rod and here is the end | |
| 18:37 | at zero centimeters and this is one centimeter down the | |
| 18:39 | rod , two centimeters down the road and so on | |
| 18:41 | all the way to 10 centimeters down the rod . | |
| 18:44 | This could be the temperature of the end of the | |
| 18:46 | rod over here , and this would be the temperature | |
| 18:48 | over here at 10 centimeters . Let's say that I | |
| 18:51 | had a flame or a blowtorch , just kind of | |
| 18:54 | heating this guy up way at the end . Then | |
| 18:57 | the end is going to be really , really hot | |
| 18:59 | over here at 10 centimeters . Really , really hot | |
| 19:01 | 10 degrees , let's call it . And then as | |
| 19:03 | I get farther away from the flame , the temperature | |
| 19:06 | is gonna go down down down . So let's say | |
| 19:07 | the end of the rod is at zero degrees . | |
| 19:09 | So this could represent a temperature kind of thing as | |
| 19:11 | well . It could represent lots of things . We | |
| 19:14 | could be stacking rocks . Um , we could also | |
| 19:17 | represent it as , let's say , this is time | |
| 19:20 | time in seconds , one second , two seconds , | |
| 19:22 | three seconds , four seconds . And this is the | |
| 19:24 | temperature in the room going up up , up , | |
| 19:26 | up , up . Maybe somebody is turning the , | |
| 19:29 | turning the knob on the , on the air conditioner | |
| 19:32 | , making it hotter and hotter and hotter . But | |
| 19:34 | the difference here is noticed in the previous examples when | |
| 19:37 | it was just a line , the temperature would be | |
| 19:40 | going up the same amount every second here . The | |
| 19:42 | temperature starts off really , really slow and it goes | |
| 19:44 | really , really , really fast . So , this | |
| 19:46 | one obviously is not a line and if it were | |
| 19:49 | temperature , it's not going up the same every second | |
| 19:52 | or the same every centimeter or whatever . It's going | |
| 19:54 | up much faster at the end here . All right | |
| 19:58 | , let's take a look at the next one . | |
| 20:00 | Let's take a look at this . This one I'll | |
| 20:03 | give you a spoiler . This will be a line | |
| 20:05 | but a different kind of line . Take a look | |
| 20:07 | at one comma eight X is equal to one and | |
| 20:10 | one is equal to eight . X . Is equal | |
| 20:12 | to one is here , don't forget . This is | |
| 20:14 | the X direction . That's the Y direction X is | |
| 20:17 | one and Y is 12345678 That means there's a point | |
| 20:23 | right there . Next five comma four is X is | |
| 20:27 | equal to five , N Y is equal to four | |
| 20:31 | . All right , So 12345 for X . 1234 | |
| 20:35 | for Y . Which is a point right here . | |
| 20:39 | And actually right here , I'm actually seeing a typo | |
| 20:41 | here , I'm gonna strike through that . That's not | |
| 20:43 | the right number . This should be a one right | |
| 20:45 | there . Sorry about that . So let's plot eight | |
| 20:47 | comma one . If I were gonna write that down | |
| 20:49 | and be eight comma one , that's the correct point | |
| 20:51 | there . So X . Is equal to eight which | |
| 20:53 | we go over here and why is equal to one | |
| 20:55 | ? Forget about the nine . Why is equal to | |
| 20:57 | one ? Which means eight comma one is a point | |
| 20:59 | that lives right there . Next two comma seven X | |
| 21:03 | is equal to two and why is equal to 1234567 | |
| 21:08 | Which means there's a point right there and then four | |
| 21:10 | comma five . You can write that is four for | |
| 21:12 | X five for y , four units over for X | |
| 21:16 | . Up 512345 means there's a point right here now | |
| 21:21 | this one actually does form a line . Um and | |
| 21:25 | so we're going to connect the dots on that and | |
| 21:27 | talk about it a little bit , but this line | |
| 21:28 | is a little different , it slants the other direction | |
| 21:31 | . So let's kind of like try to do our | |
| 21:33 | best , we'll just kind of connect through here . | |
| 21:37 | So you can see that that forms an exact straight | |
| 21:39 | line . Now the difference between this line and the | |
| 21:42 | other lines that we did before the other lines went | |
| 21:44 | this way . So if you think of this being | |
| 21:46 | time along this direction and this being temperature in the | |
| 21:50 | other lines , the temperature was going up up up | |
| 21:52 | here . If you think of this as being time | |
| 21:55 | and this is being temperature , then what's happening is | |
| 21:58 | in the beginning , right when I start my clock | |
| 22:01 | , the temperature is high but it's going down down | |
| 22:03 | down down as the seconds tick by one second , | |
| 22:07 | two seconds , three seconds the temperature is going down | |
| 22:10 | down down . So you can think of this being | |
| 22:12 | , you know , like turning the temperature down in | |
| 22:15 | a house or something , or putting some kind of | |
| 22:17 | cold ice cube on something and watching the temperature go | |
| 22:20 | down down down as the seconds tick by just one | |
| 22:22 | example , just trying to give you something to anchor | |
| 22:26 | this . You understand what we're using it for ? | |
| 22:28 | All right , And here is our last one . | |
| 22:30 | Uh We have the 1st 10.0 comma eight , x | |
| 22:35 | zero and y is equal to eight . Now notice | |
| 22:38 | we've changed things a little bit . Let's write down | |
| 22:40 | zero , comma eight and all the previous ones we | |
| 22:44 | said it's 123 all the way to 10 , 123 | |
| 22:47 | All the way to 10 . Here , we have | |
| 22:49 | changing the scale of a little bit . Notice that | |
| 22:52 | 02468 10 All the way to 20 and same thing | |
| 22:56 | up here . Why do we do that ? So | |
| 22:57 | I could put bigger numbers but don't forget that . | |
| 22:59 | Right between zero and two . Like right here , | |
| 23:03 | This is the number one , right between two and | |
| 23:06 | 4 . Don't forget . Right here is the number | |
| 23:09 | three . I'm just not writing every number because then | |
| 23:12 | it'll be cluttered . So the way you plot this | |
| 23:14 | is you look at the numbers zero comment eight x | |
| 23:17 | zero right here . Why is 82468 eights right here | |
| 23:22 | . And so I just put a dot right there | |
| 23:24 | . If you were plotting the 824680.0.70 comma seven , | |
| 23:28 | it would be between six and eight , it would | |
| 23:30 | be right there . But we don't have that here | |
| 23:33 | . Four comma 14 , that means X is equal | |
| 23:36 | to four , Y is equal to 14 . X | |
| 23:39 | is equal to four is right here . Don't forget | |
| 23:42 | this is the X direction and this is always the | |
| 23:44 | Y direction . It's always like that one graphing . | |
| 23:48 | So we have four comma 14 , here's four and | |
| 23:51 | we go up until we read 14 off in this | |
| 23:54 | direction , which means there is a dot right there | |
| 23:58 | . Next we have X is equal to eight . | |
| 23:59 | Why is 18 ? Here's X is equal to eight | |
| 24:02 | , Y is equal to 18 . You just go | |
| 24:04 | up to you read 18 there and you put a | |
| 24:07 | dot right there . Next we have 12 comma 14 | |
| 24:12 | 12 for X . And then we go up for | |
| 24:15 | 14 which means we land right there , put a | |
| 24:17 | dot right there and then 16 comma 8 , 16 | |
| 24:20 | for X . Go to 16 and then 2468 means | |
| 24:24 | I have a dot right here . So again , | |
| 24:27 | these are not gonna obviously form a line of any | |
| 24:29 | kind . You can't draw a line there and I'm | |
| 24:32 | not gonna draw a perfect curve either . So what | |
| 24:33 | you do is just try to , to kind of | |
| 24:37 | go through there . It's a curved kind of deal | |
| 24:42 | . And again , I didn't go through all the | |
| 24:43 | points exactly , but you can see it kind of | |
| 24:44 | goes upside down , it's not going to form a | |
| 24:47 | straight triangle , it's going to do some kind of | |
| 24:48 | curve thing over here . And what could this represent | |
| 24:52 | ? Just off the top of my head . Let's | |
| 24:54 | say you have a rod here , right , a | |
| 24:57 | rod and you have a blowtorch right in the middle | |
| 25:00 | , right here , making it really , really , | |
| 25:01 | really hot . So at this distance eight centimeters in | |
| 25:04 | , it's really , really hot if this is temperature | |
| 25:06 | and then on either side of the flame it's getting | |
| 25:09 | colder and colder . That's why it's going down . | |
| 25:12 | So what we use graphs for the reason why we | |
| 25:15 | plot points and we connect the dots is because when | |
| 25:19 | we see pictures , we can understand what's happening a | |
| 25:22 | lot easier than just looking at numbers . I mean | |
| 25:24 | , seriously , if I cover this up and I | |
| 25:26 | give you these numbers , no one is gonna look | |
| 25:28 | at that and understand what's happening . If I cover | |
| 25:31 | this thing up and I just look at numbers , | |
| 25:33 | no one is going to understand what's happening . But | |
| 25:35 | if I draw a picture like this and I draw | |
| 25:38 | a picture like this , then depending on what your | |
| 25:40 | problem is , it helps you visualize , oh , | |
| 25:43 | temperatures high right here and then the temperature is falling | |
| 25:46 | off or something like this . Like I've been trying | |
| 25:48 | to explain to you . And as you go farther | |
| 25:50 | and farther through math , you'll learn to graph these | |
| 25:52 | things and use the graphs to solve problems . When | |
| 25:55 | you open up math books and engineering books and science | |
| 25:59 | books in the future , you will see lots and | |
| 26:01 | lots of graphs because it helps us visualize what's going | |
| 26:05 | on . So we started here at the beginning with | |
| 26:07 | what is a point . We talked about an ordered | |
| 26:10 | pair . An ordered pair is just a number , | |
| 26:12 | common number X . Comma lie a coordinate plane , | |
| 26:15 | how we plot the points and how we connect the | |
| 26:17 | dots to understand what's happening . I'd like you to | |
| 26:20 | sketch all of these yourself , grab a sheet of | |
| 26:22 | paper and do your best to sketch them and then | |
| 26:24 | follow me on to the next lesson . We'll wrap | |
| 26:26 | up our practice with graphing ordered pairs . |
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Learn Graphing, Coordinate Plane, Points, Lines, X-Axis, Y-Axis & Ordered Pairs - [5-7-1] is a free educational video by Math and Science.
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