Question

two parallel lines are graphed on a coordinate plane.how many of the lines could represent proportional relationship?Explain.

Answer 1

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.)

Answer 2

Solution:

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.