Two – Point Form
The equation of the line passing through the point (x1,y1) and (x2,y2) can be written as :
Proof:
Since we know any two points on the line, we can write the slope of the line as
m = (y2-y1) / (x2-x1)
And we also know from point slope form that
y-y1 = m(x-x1)
Substituting the value of m in the above equation, we get
y-y1 = ((y2-y1) / (x2-x1) * (x-x1)
Example 1.Write the equation of the line passing through (5,6) and (6,7)
Solution:
Putting the value of (x1,y1) as (5,6) and (x2,y2) as (6,7) , we get
y – 6 = (7-6)/(6-5) * (x -5)
y – 6 = 1* (x – 5)
y = x + 1
Example 2.Write the equation of the line passing through (0,5) and (5,5)
Solution:
Putting the value of (x1,y1) as (0,5) and (x2,y2) as (5,5), we get
y – 5 = (5-5)/(5-0) * (x -0)
y = 0
Forms of Two-Variable Linear Equations – Straight Lines | Class 11 Maths
Line is the simplest geometrical shape. It has no endpoints and extends in both directions till infinity. The word “straight” simply means without “bend”. The gradient between any two point on the line is same. Hence, we can say that, if the gradient between any two points on the line is same, then the locus is a straight line. So let’s see what are the different ways in the line can be represented.