for 2 variable to share a proportional relationship it should follow the equation;
y = mx
where y and x are the 2 variables and m is a constant value
directly proportional means when one variable increases or decreases the other variable too increases or decreases by the same amount.
a)
2 bracelets sold for $3
1 bracelet costs - 3/2
therefore 3 bracelets would cost 3/2 * 3 = $4.5
but the cost of 3 bracelets in this case is $6 therefore this is not a proportional relationship
b)
time taken for 4 miles - 20 minutes
time taken for 1 mile - 20/4
Therefore 6 miles time taken = 20/4 * 6 = 30 minutes
but it has taken only 24 minutes to run 6 miles therefore this is not a proportional relationship
c)
number of glasses in 9 cases - 27
glasses in 1 case - 27/9
therefore glasses in 27 cases - 27/9 * 27 = 81 glasses
in the given scenario , 81 glasses were packed in 27 cases therefore this is a proportional relationship
d)
number of pencils in 2 boxes - 8
number of pencils in 1 box - 8/2
number of pencils in 8 boxes - 8/2 * 8 = 32
however in this case only 16 pencils in 8 boxes so this too is not a proportional relationship
correct answer with a proportional relationship is C