G'day welcome to the TecMath channel.
What we are going to be having a look at in this video is linear equations, moveover,
we are going to look at the linear equation.
Linear equations as you'll remember, these are equations that if you were to plot the
x and y values on a graph, on an axis, you'll end up with a nice straight line.
So what is the linear equation and why is it so handy?
I'll show you right now.
The linear equation is this one here - you've probably seen this one or a variation thereof
- it looks like this: y equals mx plus b, or you might have seen y equals mx plus c
or a variation thereof.
Pretty much all linear equations can be brought back to this particular equation.
And once you know how to look at this equation and analyse it - what the m and the b mean
here, you can tell a whole lot about this particular linear equation - just by looking
at the equation itself.
So, I'm going to give you an example of this.
So I'm going to use an example to explain this.
So the example I'm going to use is this one here: y equals 2x plus three.
Okay we'll work first off the xy values and that sort of thing, put them on a graph, and
then I'll show you a couple of key things you can tell off the equation itself.
So first off if we were to do this, let's put in the x values.
X is -3, so -3 times two is minus 6, plus three is minus three.
And then we have x is minus two, minus two times two is minus four, plus three is minus
one.
And then we have x as minus one, minus one times two is minus two, plus three is positive
one.
We're going up by twos each time, you're probably going to notice that already, so zero times
two, is zero, plus three is three.
And this one's going to be five, this one will be seven and this one will be nine.
And I could plot these on a graph, ok, so on the axis I have over here minus three and
minus three, we have minus two on the x and minus one on the y, so minus two on the x
and minus one on the y.
We have minus one and positive one, ok that's up here.
We have zero, and on the zero we cross at three.
At the value of of one we have five, y is five.
And at two we have seven, and I'm not going to be even able to fit that there, but you're
going to see we have a nice straight line here - hence the word linear equation, once
again.
But..without having to plot it each time you're going to notice a couple of things - first
off you might notice that where x equals zero ,where we cross this y axis here, is this
number here.
This here is known as the y intercept.
This is the value where x equals zero, and therefore it is what y equals.
And it's pretty simple because if you make x equal zero, it will say what y equals here
- if x equals zero, y will be equal to three.
Ok and that's a fairly common feature here, and this...b here is the y intercept.
The other thing we can see here is this number here -this coefficent here, and what that
does is that tells us how steep the graph is...ok?
So, you're going to notice this two here, as we across one, we're going up each time
here by two - up positive two each time, and as we go across one, we go up two.
This is the gradient - this is known as the known as the gradient - I'll put that in a
different colour -and what that means, quite often we think of this being the rise over
the run - and the way I think about this that this goes, it rises two, for every one it
runs across, and that's what this here tells us.
The other thing this tells us - you'll notice if it had of been a negative two, that this
graph would go downwards -so that's the linear equation here - this one here and it tells
us a whole bunch of things.
So let's look at a couple of examples just to see how handy this particular equation
is.
OK so say we had this particular graph here: y equals x plus four.
Now the first thing we can tell is that if x equals zero, the y intercept here is at
four.
So if x equals zero, at this particular point here, y is equal to four, so the graph crosses
over this particular point here.
The other thing we can see is the gradient here - the gradient in front of this x here
- which is going to be equal to one.
This is one x plus four,so this means the rise over the run, for every one we go across
we go up one, we go across one we go up one.
Ok so we go across one to one, to x equals one, we're going to be at five here.
We go across to two, we're going to be at six.
If we go across to three, we're going to be at seven.
Moreover we go back this way, we're going to be down similar sort of thing, so we're
going to have this graph that looks like this.
Ok , a nice straight line that looks like this.
Ok, anyway, what about we have a look at another one?
Say we had a graph that was this one - y equals minus two x take away three.
Now first thing we can tell where this y intercept is, because where x equals zero, y is equal
to negative three.
Straight away we can see this straight away.
The other thing we can see is the gradient - this is the rise over the run.
This minus here tells us that instead of going up this way, that this graph is going to be
going down - so that this means the rise over the run - the rise over the run, which is
the way Iike to think about this, is going to be, it's going to go down two, for every
one it goes across.
So, it's going to go down two for every one it goes across.
It's going to go down two for the next one one it goes across.
This one's going to be here, this one's going to go up here like this and we're going to
end up with a line going up like this.
Now that's just off having the equation - without drawing up any little table s or anything
like that - how handy is that right?
In future videos we're going to show how to be even more precise with these graphs and
a couple of other little things you can do, but that's the linear equation - probably
really one of the most important things to remember if you were doing linear equations.
OK so hopefully that video was of some help....see you next time.
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