Given:
The different sets of ordered pairs in the options.
To find:
The sets of ordered pairs that show equivalent ratios
Solution:
The set of ordered pairs show equivalent ratios, if
[tex]\dfrac{y}{x}=k[/tex]
Where, k is a constant.
For option 1,
(1, 2), (2, 3), (4, 7)
[tex]\dfrac{2}{1}\neq \dfrac{3}{2}[/tex]
For option 2,
(2, 2), (4, 4), (6, 6)
[tex]\dfrac{2}{2}=\dfrac{4}{4}=\dfrac{6}{6}=1=k[/tex]
The set of ordered pairs (2, 2), (4, 4), (6, 6) show equivalent ratios.
For option 3,
(3, 1), (4, 1), (5, 1)
[tex]\dfrac{1}{3}\neq \dfrac{1}{4}[/tex]
For option 4,
(4, 1), (8, 2), (12, 3)
[tex]\dfrac{1}{4}=\dfrac{2}{8}=\dfrac{3}{12}=k[/tex]
The set of ordered pairs (4, 1), (8, 2), (12, 3) show equivalent ratios.
For option 5,
(2, 1), (4, 3), (5, 4)
[tex]\dfrac{1}{2}\neq \dfrac{3}{4}[/tex]
So, sets of ordered pairs in options 1, 3 and 5 does not show equivalent ratios.
Therefore, the correct options are 2 and 4.
