Graphing linear equations using y = mx + b (Slope - Intercept) - Free Educational videos for Students in K-12

Graphing linear equations using y = mx + b (Slope - Intercept) - By tecmath

Transcript


00:0-1	Good day . Welcome to take Math Channel . What
00:01	we're going to be having a look at in this
00:03	video is linear equations . Moreover , we are going
00:06	to look at the linear equation linear equations , as
00:08	you'll remember these are equations . And if you were
00:11	to plot the X and Y values on a graph
00:13	on an axis , you'll end up with a nice
00:15	straight line . So what is the linear equation and
00:18	why is it so handy ? I'll show you right
00:20	now . Now the linear equation is this one here
00:22	. You've probably seen this one or a variation thereof
00:24	. It looks like this . Why equals Mx plus
00:28	B . Or you might have seen why ? Of
00:30	course , Mx plus C . Or a variation thereof
00:33	. And pretty much all linear equations can be brought
00:36	back to this particular equation and won't you know how
00:39	to look at this equation and analyze it what their
00:42	little M . And the B . Me in here
00:44	. You can tell a whole lot about this particular
00:46	linear equation just by looking at the equation itself .
00:50	So I'm going to give you an example of this
00:52	. So I want to use an example to explain
00:55	this . And the example I'm going to use is
00:57	this one here Why equals two X plus . That's
01:03	right . Okay . So we'll work out first off
01:06	the xy values and that sort of deal , we'll
01:08	put them on a graph and then I'll show you
01:10	a couple of key things that you can tell off
01:12	the equation itself . So first off everyone to do
01:14	this , let's put in the X values X is
01:16	minus three , so minus three times two is minus
01:19	six plus three is minus three . And then we
01:23	have x minus two minus two times two is minus
01:26	four plus three is minus one . And then we
01:29	have X -1 -1 . Times two is -2 plus
01:34	three is positive one . We're going up by twos
01:37	each time . You're probably gonna notice that already .
01:39	Okay so zero times two , zero Plus three is
01:44	3 and this one is going to be five .
01:46	This one will be seven and this one will be
01:49	nine . And I can plot these on a graph
01:51	. Okay , so on the axes I've got over
01:53	here minus three and minus three , we have minus
01:57	two on the X . And we have minus one
01:59	on the y . So minus two on the X
02:01	. M minus one on the Y . We have
02:04	minus one and positive one . Okay , that's up
02:08	. Yeah we have zero on the zero , we
02:11	cross it three . The value of one , we
02:13	have five X is five and two . We have
02:18	seven and I I'm not even gonna be able to
02:20	fit that . They're going to see we have a
02:22	nice straight line here . Yeah . Hence the word
02:26	linear equation once again , but without having to plant
02:30	it , each time , you're gonna notice a couple
02:31	of things . First off , you might notice that
02:34	where X equals zero , where we cross this y
02:36	axes here is this number here . This year is
02:40	known as the Y intercept . This is the value
02:45	where X equals zero and therefore what why calls .
02:49	And it's pretty simple because if you make X equals
02:51	zero , it will say , well , why does
02:53	he have actual equals zero ? Why is going to
02:54	be equal to three ? Okay . And it's a
02:56	fairly common feature here . And this be here is
02:59	the y intercept . The other thing we can see
03:01	here is this number here . This are coefficient here
03:06	. And what that does is that tells us how
03:08	steep the graph is . Okay , so you're going
03:12	to notice this to here ? Well , as we
03:15	go across one , we're going up each time here
03:18	by two , we're going positive to each time positive
03:23	to positive to positive two . And as we go
03:25	across one here we go up to this is the
03:28	gradient . This is known as the gradient with that
03:31	in a different color . Okay , This one here
03:33	is the gradient and what that means quite often we
03:38	think about this being the rise over the run .
03:41	And the way I think about this is this goes
03:44	across , it rises to for everyone that it runs
03:48	across . Okay . And that's what this here tells
03:51	us . The other thing , it tells us also
03:53	, you'll notice if it hadn't been a negative to
03:56	that , this graph would go downwards . So that's
03:59	the linear equation here . This one here and it
04:01	tells us a whole bunch of things . So let's
04:04	have a look at a couple of examples just to
04:05	see a handy this particular equation is okay , so
04:08	say we had this particular graphia , Y equals X
04:13	plus four . The first thing we can tell is
04:17	that if X equals zero , the y intercept here
04:21	is at four . Okay , So we're X equals
04:23	zero at this particular point here , why is equal
04:26	to four ? So the graph crosses over this particular
04:29	point here . The other thing we can see is
04:31	the gradient here , the gradient in front of this
04:33	xia , which is going to be equal to one
04:36	. Okay , this is one , X plus four
04:38	. So this means the rise over the run ,
04:40	it means everyone we go across we go up one
04:43	and we go across one , we go up one
04:44	. Okay ? So we go across 1 to 1
04:46	on X equals one . We're going to be a
04:48	five year and we go across the two , we're
04:50	gonna be at six , we go across the three
04:52	, we're gonna be at seven . Moreover we go
04:55	back this way we're going to be going down a
04:58	similar sort of thing . So we're going to have
04:59	this graph that looks like this . Okay , a
05:04	nice straight line that looks like this . Okay .
05:10	Anyway , um What about we have a look at
05:13	another one . Say we had a graph which was
05:15	this one , Y equals minus two . X .
05:20	Take away three . The first thing we can tell
05:23	where this y intercept is because we're X equals zero
05:26	. Why is equal to negative three ? Okay ,
05:29	straight away we can see that straight away . The
05:32	other thing is we can see is the gradient .
05:34	Okay , this is the rise over the run Now
05:36	this minus here tells us that instead of going up
05:39	this way this graph is going to be going down
05:42	it's going to be going down to . So this
05:45	means the rise over the run , the rise over
05:48	the run , which is the way I like to
05:50	think about this is going to be it's going to
05:54	go down to for everyone , it goes across .
05:57	So it's going to go down to for everyone that
06:01	goes across , it's going to go down to for
06:04	the next one goes across , we're going to go
06:06	this way , this one is going to be here
06:08	, this one's gonna be , you know , it's
06:11	going to get up here . So like this ,
06:12	we're gonna end up with a line that looks like
06:15	this . Okay . Yeah . That's just having the
06:21	equation there without drawing up any little tables or anything
06:25	like that . Her hand . Is that right now
06:27	? In future videos , we are going to show
06:29	you how to be even more precise with these graphs
06:31	and a couple of other little things you can do
06:33	. But that's the linear equation . Probably really one
06:36	of the most important things you remember if you are
06:39	doing linear equations . Okay . So hopefully that videos
06:43	of some help . Okay , we'll see you next
06:46	time .

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