Work out linear equations easily from two points - Free Educational videos for Students in K-12

Work out linear equations easily from two points - By tecmath

Transcript


00:0-1	Good day . Welcome to Tech Math channel . What
00:02	we're going to be having a look at in this
00:03	video is linear equations . That is equations that if
00:05	we were to graph them , give nice straight lines
00:09	like this one here , specifically in this video ,
00:11	what we're going to have a look at is how
00:13	to work out the equation for this particular type of
00:16	graph , knowing only two points on it's actual line
00:20	here . Okay , so we have a Y axis
00:22	and an X axis here and knowing this X and
00:26	this Y and the value of this X and this
00:29	Y . And to do this , we're going to
00:31	be using the linear equation . That is , as
00:34	you probably remember , Y equals Mx plus B .
00:39	So just to recap what this particular equation means ,
00:42	we have the X and Y values which are in
00:44	the equation here . As you see here , we
00:46	also have em , which gives the gradient of this
00:50	particular graphia and also the B . Which is this
00:54	why interceptor aware the actual graph intercepts the y axis
00:59	. Again , all linear equations can be described by
01:01	this particular equation . So I'm going to go through
01:05	a couple of examples . Okay , so the first
01:07	particular example I'm going to have a look at is
01:09	this one here , I'm going to write down the
01:11	X and Y values . We're going to have to
01:12	X and Y . And I'm going to write them
01:14	down in this particular order X followed by the wind
01:17	. This is a standard way that we do these
01:19	. Okay , so the first one We have an
01:22	x value of one and a Y value of three
01:25	. So we have this point on this grass and
01:27	we also have a X value of three and a
01:30	Y value of five . And so I'm looking for
01:32	a linear equation that contains these points . So the
01:36	easiest way to do this , the first thing we
01:38	do is we're going to work out The gradient .
01:41	This m value would see what that equals two .
01:44	Their first off , you may know the formula for
01:47	the gradient , which is equal pretty much to the
01:49	rise over the road . That is to say how
01:53	far do we go up as we go across ?
01:55	Okay , so let's have a look at this .
01:58	The Y values described how far we're going up so
02:01	we can have a look at the difference between these
02:03	values . As I go from this one to this
02:05	one , you can see that I go from 3-5
02:07	, I'm going up so you can see now with
02:12	the X ways , how far we go across As
02:14	I go from 1-3 , I'm also going up to
02:19	. So the rise over the run here is to
02:21	over two which is equal to one . So in
02:24	our equation here we have Y . Is equal to
02:27	and I'm going to put a little Why is equal
02:30	to one x plus B . And we're gonna find
02:34	out what the eagles and how do we do this
02:37	? Well , this is fairly simple because we just
02:39	substitute one of these particular values into our equation here
02:44	. Okay , so I'm just going to choose the
02:46	first one here . If why ? Which is three
02:50	is equal to white X one times one is one
02:53	. What would I add to one to make this
02:56	equation true . And you'd say okay , I had
02:58	to do this equation . All right , So this
03:02	is going to be equal to plus two . Okay
03:05	, Why is equal to one ? X plus two
03:08	? And you can double check this by substituting in
03:10	the values on this one . If I have to
03:12	say for our equation here , Now that is Y
03:15	equals x plus two if x equals three . So
03:19	why equals three times one ? Three times one which
03:23	is three plus two is equal to five is equal
03:26	to five , So 3-plus 2 is fine . So
03:29	our equation here is correct and that's how I work
03:33	at the equation based upon three points . Let me
03:36	go through one more example of this . Okay ,
03:39	So say we have an X . Value of two
03:42	and a Y value of negative four and that's on
03:44	our equation or on our graph . And the next
03:47	one we have is we also have a point where
03:48	it's minus one on the X . And the five
03:51	. Okay . So the first thing you're going to
03:53	remember you remember is we work out the gradient m
03:57	which is equal to the rise over the run the
04:00	rise over the road . Okay ? So as we
04:04	go from negative 4 to 5 you'll see . Okay
04:07	we've gone from 4 to 0 which is four and
04:09	then five more . So we've gone up nine positive
04:12	nine . And as we've gone from this is the
04:16	run here . As we've gone from 22 negative one
04:19	you can say hey what's that ? We haven't gone
04:20	up , we've actually gone back three . We've gone
04:22	down three . So this is a negative three .
04:25	Okay so nine Over -3 equals -3 . Our equation
04:30	here is going to be why Equals -3 X .
04:37	Plus something or minus something . So let's work out
04:40	what that something is . So let's substitute in this
04:44	value here . Okay so Why ? Which is five
04:48	here is equal to negative one times three X .
04:53	Negative one times negative three . That's right . Plus
04:58	what number ? And you can say okay three plus
05:00	two equals five . So this has to be a
05:02	plus two . Does it work out ? Let's double
05:05	check on this particular point here . So two times
05:09	-3 was born , six Plus two is -4 .
05:14	Which is the same as this . So that means
05:17	this is correct and this is our equation anyway .
05:20	That's how easy it is to do this particular thing
05:23	. It's fairly simple . Right ? Working at the
05:26	new equation based on two points made , I don't
05:28	even have to draw any grass for that . But
05:31	you can always practice during the graphs as well anyway
05:34	. Hopefully find that video . I he found this
05:36	video informative . We'll see you next time . Bye
00:0-1	.

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