Linear equation from graphs - Free Educational videos for Students in K-12

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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