Students so far, we have seen these two ways in which we represent a straight line right now, let's
learn the third way in which we represent a straight line in this video.
So that would be why is equal to M. X plus C now M is the slope.
And we learned what we mean with the slope soon and C stands for the Y intercept, which is the value
when X is equal to zero.
All right, let's try to understand this equation in a better manner.
OK, so for that, first, we need to understand what do we mean with the slope of a line?
All right, let's try to understand that now over here I have a line and let me have another line over
here that goes like this right now over here.
The angle is three to one, right.
And this angle is the tattoo.
Now, this line has a negative slope.
What do we mean with that?
It's a decreasing function.
As the X increases, you can see that the Y value keeps on decreasing.
Right over here, you have a positive slope.
That is as the value of X increases, the value of Y keeps increasing.
So this over here is a decreasing function and this over here is an increasing function.
All right.
So over here we have defined the angles.
This is angle to one.
This is theta two.
Now, the slope is obtained by finding Tante to.
All right, now, when you find the slope, you will find that in this case, Santita one will give
you a negative value.
And remember, you can see more about an internal metric.
Now, over here you will get to which is a positive value.
Now, remember, these type of angles which are taken in this way are called a positive angle.
And this is a negative angle.
But typically that's not required in questions.
But again, this is a negative angle.
This is a positive angle.
That's right.
Down of this angle will give you a positive value.
And this is a negative angle.
That's why down of this angle will give you a negative value, but in a visual manner.
We can understand it like this over here.
As X increases, Y decreases.
Right.
Because these values of light are negative.
So it's a decreasing function and hence the slope is negative all year.
As X increases, Y increases right at point for X equals four, you have Y, it is around to right at
point five, X equals five, you'll have Y around four.
So you can see that it's an increasing function and hence it has a positive slope.
Now remember, slope is given by fan of Peter already having identified this.
Let's get back to our equation.
We have seen that slope describes this land of the line and we have seen that it's given by 10 of the
top right slope is given by 2010, where Theta is the angle that the line makes with the x axis.
All right.
Now, let's take an example of an equation of a line.
You have three Y is equal to twelve minus for X.
All right.
Now, over here, I can say that Y is equal to.
Minus four by three X, plus 12 by three, which is equal to or right.
It's the same equation.
I just divide this by three and I divide this side also by three by half way over here and all I have
12 by three.
That's four and minus four by three X.
That's what we have over here.
All right.
Now, if you have an equation like this compared with this form over here, you can see that minus four
by three is the slope and four is the Y intercept.
And what do we mean when we say that minus four by three is the slope?
It means it describes the end of the line.
And also it means that 20 to one is equal to minus four by three.
All right.
So we have seen the third way in which a line is described, which is why is equal to and makes policy.
Right.
And over here, M is the slope and C is the Y intercept.
Now, let me take that over here.
Now, over here, we have seen this interesting form weather wise of the form and makes policy.
Right now we are going to see the two point form of writing a line.
And along with this, we will learn a little bit more about the slope that is we have seen before that
the slope is Dante right now, or you will see another way in which we can identify the slope already
or here.
I have two points.
Let me tell them as x1 why one and x2 y2.
But these are these two points.
Now I can write the equation of this line as Y minus Y one by X, minus X one where you take any point
as the first point is equal to Y to minus Y one by x2 minus x1.
And remember any point can be taken as the first point and any point can be taken as the second point.
All right, let's try to apply this equation in a real case.
Let this point be zero four and this point B three zero.
When we applied over here we get Y minus four divided by X, minus zero is equal to zero, minus four
by three minus zero.
Right.
So that gives us Y minus four.
Divided by X is equal to minus four by three.
Now if you take X over here and you take this minus four also to this side, this becomes Y minus four
by Y is equal to minus four by three X plus four, which is the same equation which we had over here.
Right.
So this is called the two point four of often line.
So to write this equation, you need two points.
That's why it's called a two point four.
Now, an interesting point to note over here is this part over here that is Y to minus Y by X to minus
X, one is the slope of the line.
So we have seen before that slope is given a study done.
Now you can find the slope like this.
Also, if you have two points, you can find the slope as Y two minus Y, one by X2 minus X1.
All right, let me take this over here.
So we have learned the generic form.
We have learned the form where we write X divided by the X intercept plus Y divided by the Y intercept
is equal to one.
And the next form that we learned about is Y is equal to imex policy.
And this is the two point form that we discussed.
And remember, we discussed that the slope of this line where two points are given is equal to Y to
minus Y, one by X2, minus X one.
So in this case, if the point is zero four and three zero, what would be the slope?
It's zero minus four by three minus zero.
Right.
That is equal to minus four by three.
Now you know the slope.
Now can you write the equation of the line using this form?
That is why is equal to and makes policy.
Yes, we can do that.
Right, because we know M is minus four by three.
So the equation becomes why is equal to minus four by three X plus the Y intercept.
Now what is the Y intercept over here.
Over here you can see that this is the Y intercept, right.
When X is equal to zero, Y is equal to four.
So the Y intercept is four.
So the equation of the line becomes Y is equal to minus four by three X plus four.
All right, let's quickly summarize, we have learned four ways of writing the equation of a line.
This is the generic form, then this is the form where we use X and Y intercepts.
This is the form where we write Y is equal to mix policy.
And we learned about the PowerPoint form where the equation of the line is given us Y minus Y one by
X, minus X one is equal to Y two minus Y, one by X2 minus X one.