Question

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

Answer 1

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.

Answer 2

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.)