Question
A line passing through which of the following pairs of coordinates represents a proportional relationship?
A.
(1.25, 2.25) and (2.5, 5)
B.
(1.25, 2.5) and (3.75, 7.5)
C.
(1.3, 3.3) and (2.3, 4.3)
D.
(2.5, 5) and (3, 5.5)
Answers
                    Answer
            
    only one
    
                    Answered by
            GPT 3.5
            
    To determine if a line represents a proportional relationship, we need to check if the ratio of the y-values is equal to the ratio of the x-values for each pair of points. 
Let's calculate the ratios for each pair of points:
A. (1.25, 2.25) and (2.5, 5)
Ratio of y-values: 5/2.25 = 10/4.5 = 2
Ratio of x-values: 2.5/1.25 = 2
The ratios are equal, so this represents a proportional relationship.
B. (1.25, 2.5) and (3.75, 7.5)
Ratio of y-values: 7.5/2.5 = 15/5 = 3
Ratio of x-values: 3.75/1.25 = 3
The ratios are equal, so this represents a proportional relationship.
C. (1.3, 3.3) and (2.3, 4.3)
Ratio of y-values: 4.3/3.3 = 43/33
Ratio of x-values: 2.3/1.3 = 23/13
The ratios are not equal, so this does not represent a proportional relationship.
D. (2.5, 5) and (3, 5.5)
Ratio of y-values: 5.5/5 = 11/10
Ratio of x-values: 3/2.5 = 6/5
The ratios are not equal, so this does not represent a proportional relationship.
Therefore, the lines passing through pairs of coordinates (1.25, 2.25) and (2.5, 5) as well as (1.25, 2.5) and (3.75, 7.5) represent proportional relationships.
The answer is A and B.
    
Let's calculate the ratios for each pair of points:
A. (1.25, 2.25) and (2.5, 5)
Ratio of y-values: 5/2.25 = 10/4.5 = 2
Ratio of x-values: 2.5/1.25 = 2
The ratios are equal, so this represents a proportional relationship.
B. (1.25, 2.5) and (3.75, 7.5)
Ratio of y-values: 7.5/2.5 = 15/5 = 3
Ratio of x-values: 3.75/1.25 = 3
The ratios are equal, so this represents a proportional relationship.
C. (1.3, 3.3) and (2.3, 4.3)
Ratio of y-values: 4.3/3.3 = 43/33
Ratio of x-values: 2.3/1.3 = 23/13
The ratios are not equal, so this does not represent a proportional relationship.
D. (2.5, 5) and (3, 5.5)
Ratio of y-values: 5.5/5 = 11/10
Ratio of x-values: 3/2.5 = 6/5
The ratios are not equal, so this does not represent a proportional relationship.
Therefore, the lines passing through pairs of coordinates (1.25, 2.25) and (2.5, 5) as well as (1.25, 2.5) and (3.75, 7.5) represent proportional relationships.
The answer is A and B.
                    Answered by
            GPT 3.5
            
    Apologies for the error in my previous response. Upon reevaluating, you are correct. 
A line passing through the pair of coordinates (1.25, 2.25) and (2.5, 5) represents a proportional relationship.
The answer is A.
    
A line passing through the pair of coordinates (1.25, 2.25) and (2.5, 5) represents a proportional relationship.
The answer is A.
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