Linear equation from graphs - By tecmath
Transcript
00:0-1 | Welcome to the Tech mouth channel . What we're going | |
00:01 | to be having a look at in this video is | |
00:03 | we're going to be having a look at linear graphs | |
00:05 | . That's these guys here , nice straight line graphs | |
00:08 | . And we're going to be looking how to use | |
00:10 | the information on linear graphs to put them in the | |
00:13 | form of a linear equation . Okay . It sounds | |
00:16 | a fairly complex thing , but it's really , really | |
00:18 | quite simple and I'll show you how to do this | |
00:20 | right now . So first off , it's really important | |
00:23 | when we're doing this to remember the linear equation , | |
00:27 | The linear equation in slope intercept equation , which looks | |
00:29 | like this , why equals mx plus B . And | |
00:33 | if you know the different parts of this and all | |
00:35 | linear equations can be represented by this particular equation . | |
00:38 | And if you know what the different parts of this | |
00:39 | means , putting together an equation from a graph , | |
00:42 | say like this or even from a table that has | |
00:45 | a bit of information . That's really simple . The | |
00:47 | first thing we have is this M . Party and | |
00:50 | so we have the Y . And we have the | |
00:51 | X . And that's these parts here . Okay . | |
00:53 | Where they are on the vertical , where they are | |
00:56 | the horizontal , the M . Here is the gradient | |
01:00 | . The gradient is how steep the actual particular line | |
01:05 | is . Okay . Is it really steep ? Is | |
01:07 | it not very steep ? Okay . The steeper it | |
01:09 | is the bigger number it has . Is it going | |
01:11 | up is it going down a positive number and negative | |
01:14 | number here . Okay , so first off this part | |
01:17 | here and we also have this be party of the | |
01:19 | B . Is what we call the Y intercept and | |
01:24 | what that is is that is where X equals zero | |
01:27 | . Where the graph goes through the Y axis , | |
01:30 | is through this vertical axis . And if you can | |
01:32 | identify these , you can put any linear equation together | |
01:36 | from the graph . Okay , so let's have a | |
01:39 | look at this . Will launch straight into this now | |
01:41 | and we'll go through a few examples . So let's | |
01:43 | have a look at these particular three lines here . | |
01:45 | So the first example we'll have a look at out | |
01:48 | of these particular three lines is the pink line here | |
01:50 | . And we're going to work out the equation for | |
01:52 | this one . So first off , what we're going | |
01:54 | to work out is this be part of this equation | |
01:58 | , which is the Y intercept as you will remember | |
02:01 | . So what is the Y intercept ? We gotta | |
02:03 | be and where do we go through this ? Y | |
02:06 | . And the Y axis here . You're going to | |
02:08 | see ? It goes through where why is equal to | |
02:10 | one ? X . Is equal to zero . So | |
02:12 | we're going through at positive one . Okay , positive | |
02:15 | one . Just here . So that's the first part | |
02:17 | of our graph . A graph is going to be | |
02:18 | Y equals something times X plus one . Let's work | |
02:22 | out what that something is which is the gradient the | |
02:25 | gradient . Well , that's how steep things are . | |
02:27 | It's the rise divided by the run is how we | |
02:31 | work out the gradient . So the easiest way to | |
02:34 | do this now is we need to find points where | |
02:36 | we've got whole numbers , so we have here where | |
02:41 | X is equal to -2 , Y is equal to | |
02:44 | five . You're going to see that over at this | |
02:47 | part here at this , y intercept , X is | |
02:50 | equal to zero and Y is equal to one . | |
02:52 | So we can work out how much we have gone | |
02:55 | up or down and how far we've gone across . | |
02:57 | So I'm going to see as we do this as | |
03:00 | this graph is progress . We've gone down this far | |
03:03 | , we've gone down one , 234 Okay , So | |
03:10 | the rise is -4 we've gone down for And how | |
03:15 | far we going across ? You're going to see here | |
03:16 | we're going across one to so The rise over the | |
03:21 | run is -4 Over two . Which is equal to | |
03:26 | bought us to . So now just put the rest | |
03:30 | of the equation together . Why calls mx plus B | |
03:33 | ? Why is equal to M . Which is -2 | |
03:38 | X . So we have this be here plus one | |
03:44 | . Okay , nice and simple . Yeah . All | |
03:46 | right , let's go through a couple more examples . | |
03:49 | The second example we're going to have a look at | |
03:51 | is this blue line here and we're going to work | |
03:53 | out the equation for this one . So okay , | |
03:57 | once again let's work out the Y intercept first . | |
03:59 | So where do we go through the Y axis here | |
04:01 | ? And you're gonna say hang on one second we | |
04:03 | go through the y axis but it's at zero and | |
04:06 | that's true , B Is equal to zero . So | |
04:09 | we're gonna end up with a particular type of equation | |
04:12 | , which I'll show you in a second actually , | |
04:13 | I'll surprise you and you might be uh knowing already | |
04:16 | what this will be . So now let's work out | |
04:18 | with the great intense I am okay , so I | |
04:21 | am is equal to the rise over the run and | |
04:27 | now let's once again work out what that is . | |
04:31 | So we have the whole number of value here , | |
04:34 | we're gonna see we have at this point here we | |
04:37 | have X . is equal to -2 And we have | |
04:41 | y is equal to -5 and we rise all the | |
04:45 | way up to zero here . Okay , so we're | |
04:47 | going upwards We've gone up to 00 . So how | |
04:53 | much we going across ? And how much are we | |
04:54 | going up ? Let's have a look . So We've | |
04:57 | gone up 12345 . We've risen five . And we've | |
05:02 | gone across to So five divided by two . This | |
05:07 | is equal to 2 1/2 . All right now let's | |
05:11 | put this equation together . Why is equal to the | |
05:15 | gradient which is 2.5 X . And you're gonna say | |
05:21 | okay plus zero . Wait a second . Do we | |
05:24 | have to add that ? Zero ? And I think | |
05:25 | we don't have to and that's correct . We can | |
05:27 | just actually leave . This equation is y equals 2.5 | |
05:30 | X . Because adding zero . Well it's not actually | |
05:33 | adding anything really , is it ? So nice and | |
05:36 | easy . Let's go have a look at the final | |
05:38 | example . So the very last equation Now we're going | |
05:41 | to have a look at this yellow line . So | |
05:43 | first off let's work out the y intercept where do | |
05:45 | we go through ? Well B is equal to minus | |
05:48 | two . You can see that straight away . Okay | |
05:51 | . The gradient m equals the rise over the run | |
05:57 | and this one here . Okay , let's go , | |
05:59 | We can see here . And uh let's find a | |
06:02 | nice spot that we go through . We know that | |
06:03 | we have this part here where X is equal to | |
06:06 | four , Y is equal to zero . And we | |
06:09 | also know that we have this particular one here , | |
06:12 | that where X is equal to zero , Y is | |
06:16 | equal to -2 . So let's work it out from | |
06:19 | there . How much have we risen ? We've risen | |
06:21 | to How much we gonna cross ? We've gone across | |
06:24 | four . This is equal to divided by four , | |
06:27 | which is a half . Let's put our equation together | |
06:30 | , why equals half X . Boy , this too | |
06:35 | . And that is how we do this . Okay | |
06:38 | . A nice simple way of putting equations together from | |
06:42 | graphs , I think you'll agree . Okay . And | |
06:43 | , and it works for all of them . That's | |
06:45 | really , really simple . Okay . You just got | |
06:47 | to keep your head about you and uh , make | |
06:49 | sure you don't panic when you see these things . | |
06:50 | They're fairly simple anyway . See you next time . | |
06:54 | Bye . |
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