You need minimum of two lines which are parallel or coincident to represent proportional relationship.
Suppose two lines in one dimensional plane is Coincident.These lines are represented by a and b. Then to represent proportional relationship between them ,we can write it as follows
a = K b
or, b= Ta, where K and T are proportionality constant.
→→Line in two dimensional coordinate plane, which passes through origin or are Coincident, represents proportional relationship.
1. 2 x + 3 y= 5
2. 4 x + 6 y =10
Line 2 = 2 × Line 1
2. y= k x is equation of any line passing through origin, where k is constant of proportionality between x coordinate and y coordinate.
It's not necessary that either one represents a proportional relationship. But if either one does, then the other one doesn't. They can't both represent such a relationship.
The graph of a proportional relationship must go through the origin. If one of a pair of parallel lines goes through the origin, then the other one doesn't. (If two parallel lines both went through the origin, then they would both be the same line.)
