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)

Answer 1

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.

Answer 2

only one

Answer 3

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.