14JUL21

Say (x1,y1) and (x2,y2) are two points on a straight line.


Consider some general point (x,y) on the line.


Let's measure slope using (x1,y1) and (x,y).

Slope = (y-y1)/(x-x1)

Again, let's meaure slope using the two given points (x1,y1) and (x2,y2).

Now, slope = (y2-y1)/(x2-x1)

But we know (y-y1)/(x-x1) must be equal to (y2-y1)/(x2-x1).

Therefore, (y-y1)/(x-x1) = (y2-y1)/(x2-x1)

This is the equation of the line.

This is called POINT FORM.


Suppose, a line cuts the X-Axis at (a,0) and the Y-Axis at (0,b).

Say, (x,y) is some general point on the line.

Now, (y-0)/(x-a)=(b-0)/(0-a)

y/(x-a)=-b/a

If this is simplified, we get (x/a)+(y/b)=1

This is called INTERCEPT FORM of a straight line.


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