Linear Equations Introduction - Free Educational videos for Students in K-12

Linear Equations Introduction - By tecmath

Transcript


00:0-1	Good day . Welcome to the Tech Math channel .
00:01	What we're gonna be having to look at in this
00:02	video is linear equations . It's gonna be part of
00:05	a series of videos . We're going to be having
00:07	a look at linear equation . So this one is
00:08	just a bit of an introduction . Uh , so
00:11	what are linear equations ? Well , these put simply
00:13	pretty much if you were to graph a linear equation
00:15	, which will show you in a second , they
00:18	come out straight law . And since they're called linear
00:19	equations are their equations . That if you look at
00:22	the relationships between the different parts of it , they
00:24	go up by very regular amount . So that that's
00:27	the reason for the straight line . So although it
00:29	straight into what an example of a linear equation is
00:32	quite commonly , you'll see one that will look like
00:35	this . Why equals two X plus one . And
00:40	if I was to graph this , okay , we
00:42	have two variables here , we have the Y ,
00:44	and we have the X . And if I was
00:46	to graph this it will come out as a straight
00:48	line . In fact , I'll tell you what ,
00:49	I'll show you this right now . So say the
00:53	easiest way to do this when we first do these
00:55	is we're going to put in a make a bit
00:57	of a table up for ex and why And we'll
01:02	put in values of X and see what why comes
01:04	out . And then we'll graph to see what happens
01:06	. Okay ? So first off I'm going to start
01:08	with -3 . They're not gonna go minus two for
01:11	x minus 10123 Okay . And we'll work out what
01:17	these are . So let's put that little grid in
01:19	to help us are you know to see what we're
01:21	doing and now we'll work out what the Y values
01:24	are . So if y equals two X plus one
01:28	or two times X two times minus three for minus
01:31	three X value two times minus three is minus six
01:34	plus one is Boris five . Okay If X equals
01:40	minus two minus two times two is minus four plus
01:44	one is minus three . If X equals minus one
01:47	minus one times two is minus two plus one is
01:52	minus one . And you're gonna see already we're going
01:54	up by two so far each time . What do
01:58	you think this one will be ? We'll have a
01:59	look if X equals zero zero times 20 plus one
02:04	is one . So we're going up by a regular
02:07	amount each time . This is a pretty normal thing
02:09	with linear equations . So we're going to go up
02:11	by regular amounts . It's going to be very uh
02:14	it's something which always happens . So the next one
02:17	you can probably guess will be a three . This
02:18	one here will be a five and that one there
02:21	will be a seven and you can check those out
02:22	. You can you can substitute the X . Values
02:25	into the equation if you want to check that out
02:28	. Okay so now I've zoomed out a bit and
02:30	put an access up so we can grab this linear
02:32	equation . We can you can see what they look
02:34	like . They're gonna see I've got two axes here
02:36	, this is an axis here , the vertical one
02:38	which is the y axes . We're gonna put the
02:40	Y values along here , that's where the y values
02:42	go . And along here you have the horizontal x
02:46	axes . Okay And so we're gonna put these values
02:50	in here and you'll see why it's called a linear
02:52	equation . So without much further ado we got where
02:55	we have an ex of minus three , we have
02:57	a wide of minus five x minus three . And
03:00	Why is it -5 ? Where X equals -2 ?
03:05	We have a wide of -3 , so -2 -3
03:09	. We have a modest one X . And a
03:11	modest one way . So they're here , you're going
03:13	to see straight away , we're going up , you
03:15	know the norse Straight line . It started off where
03:20	X is equal to zero . We have why being
03:23	equal to one where X is equal to one ?
03:26	We have y equal to three where X is equal
03:29	to two . We have y equal to five and
03:31	we're X is equal three . We have y equal
03:33	to seven . So we have this nice straight line
03:37	. I'm gonna draw freehand . We'll see how that
03:38	goes . Not too bad . It could have been
03:41	a straight a straight line . You can see this
03:42	is a nice straight line that goes through , hence
03:45	the thing linear equation . The other thing you're going
03:47	to see is if I zoom in that these are
03:50	going up by very regular amounts , Okay , you're
03:53	going to see that for the amount that we go
03:56	across one it's going up to , and we go
03:59	across one and it's going up by two . And
04:02	this is a fairly regular thing . This is this
04:05	is something that happens with linear equations . Anyway .
04:10	Uh just before the last thing , I want to
04:12	tell you this , and we are going to do
04:14	a whole bunch more things on linear equations will be
04:16	. How do you recognize a linear equation without having
04:19	to graph it up each time ? Well , it's
04:21	fairly simple and I'll tell you right now how to
04:23	do it . So how do we tell a linear
04:26	equation just by looking at it ? Well , you
04:28	can it's really simple . You're just looking for three
04:31	key things . There's three conditions that we're trying to
04:34	meet when we look at linear equations . And the
04:36	first is this linear equations can have these things called
04:40	constants . They don't have to have them . And
04:43	other equations can also have them . What is a
04:45	constant ? A constant is something like one here ?
04:47	Okay , It's one , it's always going to be
04:49	a one . It's not changing its constant . Yeah
04:52	. Other equations can also have a plus one at
04:54	the end of them and not be linear . So
04:56	this isn't the only thing we look at , and
04:58	also a linear equation doesn't have to have this ,
05:00	but it's allowed to have it . Okay , you
05:03	could have Y equals two X . And that would
05:05	also give us a linear equation . So , there's
05:09	a second condition we're gonna be looking for is where
05:11	we look at the constance and the variables . Okay
05:14	, so we can have a variable here . We
05:15	have two variables in this equation . We have why
05:18	we have X . But these variables and they can
05:21	be multiplied by a constant here . But the variables
05:25	are not raised to any power , like squared or
05:29	cubed or they're not being square rooted . I'll give
05:31	you an example here . If I was to say
05:33	this equation here , why equals X squared ? This
05:38	would not give us a linear graph . This is
05:41	not a linear equation or why equals square root of
05:45	X plus one . Okay , As a constant ,
05:49	it's allowed to have that . But this square root
05:51	thing , it means straight away that this is not
05:53	a linear equation . So if you see anything like
05:56	this , you know , straight away , these are
05:58	not linear equations . But if you just have X
06:01	. If you had something like Y equals three x
06:04	minus two , you can say , okay , look
06:07	, these are not being raised up to any powers
06:09	. And there's just some constants here . This will
06:11	be a linear equation . There's a third thing we
06:14	can also look for . Okay , and that's that
06:16	the variables are not being multiplied together . So ,
06:19	say you had something like uh X Times y equals
06:24	10 . This would not give us a linear graph
06:29	. This is not a linear equation . Okay .
06:32	Uh Okay . So , this will give us actually
06:34	a rather cool looking graphic was to draw it that
06:37	looks like this . Okay , It's not a straight
06:40	line graph . All right . So , pretty much
06:43	we're looking for those three conditions . They can have
06:46	constants that the variables aren't being squared or square root
06:49	or anything like that , and that the variables are
06:52	multiplying together . And if you fulfil those conditions ,
06:55	you've got yourself a linear equation . In fact ,
06:58	every straight line can be , uh can be represented
07:02	by this equation that you might have seen before .
07:04	You might have seen it as why equals mx plus
07:08	B . You might have seen as plus C .
07:11	Depending on where you come from . This equation is
07:13	going to be really useful . We're gonna be having
07:15	a look at the future videos and it's really ,
07:18	really good . You can tell a lot of things
07:19	about linear equations just by looking at this particular equation
07:24	. Anyway , I hope this was a fine introduction
07:27	for linear equations for you . I'm looking forward to
07:29	going through these are really like linear equations . So
07:32	we'll see you soon . Okay , bye .

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Linear Equations Introduction is a free educational video by tecmath.

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