In a proportional relationship, an increase or decrease in one variable leads to a corresponding increase or decrease in another variable. Both variables are related by a value known as the constant of proportionality.
Looking at the first equation,
x = 2y
an increase in x would lead to a corresponding increase in y. the constant of proportionality is 2
Thus, x = 2y represent a proportional relationship
Looking at 1/2 = 1/4, there is a constant factor relating both quantities. 1/2 is double 1/4. This means that the constant of proportionality is 2. Thus,
1/2 = 1/4 is a proportional relationship
Looking at a = 1/3b, the constant of proportionality between a and b is 1/3. Thus,
a = 1/3b = a proportional relationship
