## Two Point Form

Hello students, Previously we have discussed about substitution method calculator and today we are going to discuss about the equation of a line passes through two points which is also known as two point form of a line. let us assume a line AB passes through two points A (x1,y1) and B ( x2,y2 ).then the Cartesian form  of the equation can be represent as (x2-x1) * (y- y1)=(y2-y1) * (x-x1) it can also be written as (y- y1)=(y2-y1)/(x2-x1) * (x-x1) . Where   (y2-y1)/(x2-x1) represent the slope of the line with the x-axis.now let us take some examples to understand the topic of the equation of a line from two points. Find the equation of a line passes through the point (2,3) and (-3,4) . as we know the equation of a line from two points can be written as (y- y1)=(y2-y1)/(x2-x1) * (x-x1) here we consider the point (2,3) as (x1,y1) and (-3,4)as (x2,y2). By putting the values in the two point form we get (y-4) = (4-3)/ (-3-2) * (x-2). Which can further written as (y-4) = -1/5 * (x-2). By cross multiplication the equation can be written as 5(y-4) = -1(x-2). Or we can write it as 5y +x =22. This is representing the equation of a line from two points. Let us take another two point form example by considering a line passes through the point (-1,-1) and (4,3). As we consider earlier let (x1,y1) =  (-1,-1) and (x2,y2) = (4,3). By substituting the values in two point form we get           (y+1) = (3+1)/ (4+1) * (x+1). Which can further written as (y+1) = 4/5 * (x+1). By cross multiplication the equation can be written as     5(y+1) = 4(x+1). Or we can write it as 5y -4x =-1. This is representing the equation of a line from two points. I hope with the help of the examples given a above the two point form of a line will become easier to understand. In The Next Topic We Are Going To Discuss Formula For Slope Of A Line And Finding The Slope Of A Line.

In the next session we will discuss about Polar Equations of Lines and You can visit our website for getting information about college algebra help and ncert solutions for class 10 science.