Learn Intercept Formula

Learn Intercept formula is nothing but slope intercept formula. Before going to learn intercept formula we need to know why it is called so.

It is called slope intercept form because the equation includes slope and the y-intercept. So now we know the reason why it is called slope intercept form. Now coming to actual concept.....

The general form of slope intercept form is:

y= mx^+b

Where m--> slope of the line.

b --> y-intercept.

y --> y-coordinate.

x -->x-coordinate.

Formula - learn intercept formula


Slope intercept form is the simplest of all forms as we just need to plug in the values of slope(m) and y-intercept(b).

Now how are we going to get the slope??. In problems the slope might be mentioned directly or two points through which the line passes might be given. When the second case occurs slope can be find out using formula
slope(m)= (change in x)/(change in y)

Now let us consider that two points are (x1,y1) and (x2,y2)  then slope is given by

m=(y2-y1)/(x2-x1)

We have learnt how to find slope in the slope intercept form. now the next one to be calculated is y-intercept(b).
For this we need to plug the point through which the line passes.

This point will be mentioned in the question. If slope is m and the point is (p,q) then

plugging these values in slope intercept form we get

q= m*p+b

==> b= q-mp.

Now we have slope and y-intercept substituting these values we get slope intercept form.

I think to learn intercept form is very easy  and... cool

Examples on learn intercept formula


Ex1:  What is slope intercept form of line having slope 2 and y-intercept 3?
Sol1:

Given slope (m)=2, and y-intercept (b)=3

Plug these values in slope intercept form y=mx+b

Then        y= 2*x+3

y=2x+3.

So slope intercept form of a line having slope 2 and y-intercept 3 is

y=2x+3

Ex2:  What is slope intercept form of line passing through the point (2, 3) and having a slope of 4.
Sol 2:

Here we have slope = 4 and y-intercept is not mentioned but the point through which line passes is given.

Plug m=4 and (x,y)= (2,3) in the slope intercept form y=mx+b.

Then we get

3=4*2+b.

==>b+8 =3

==>  b=3-8=-5

So y-intercept is b=-5 and we have slope as m=4.

Plugging these in slope intercept form we get

y= 4x -5.

Ex3:  Express the equation 3x+4y+5=0 in slope intercept form.
Sol 3:

The given equation is 3x+4y+5=0.

In order to convert it in to slope intercept form bring y terms on one side and the remaining terms to other side.

For this subtract with 3x and 5 on both sides

3x+4y+5-3x-5=-3x -5

By doing this 3x and 5 get cancelled and the equation becomes

4y= -3x-5

Divide both sides by 4

4y /4 = (-3x-5)/4

y=-(3/4)x  - 5/4

Thus the slope intercept form of 3x+4y+5=0 is y=-(3/4)x  - 5/4