Answer: The second table
Step-by-step explanation:
For the table to show proportional relationship between x and y , then they must have a common ratio. that is x/y must be the same throughout
Table 1
[tex]x_{1}[/tex] = 1 [tex]y_{1}[/tex] = 2
[tex]x_{2}[/tex] = 3 [tex]y_{2}[/tex] = 5
[tex]x_{3}[/tex] = 4 [tex]y_{3}[/tex] = 8
[tex]x_{4}[/tex] = 7 [tex]y_{4}[/tex] = 14
[tex]\frac{x_{1}}{y_{1}}[/tex] = 1/2
[tex]\frac{x_{2}}{y_{2}}[/tex] = 3/5
[tex]\frac{x_{3}}{y_{3}}[/tex] = 4/8 = 1/2
[tex]\frac{x_{4}}{y_{4}}[/tex]= 7/14 = 1/2
Since the ratio is not the same throughout , then x and y are not proportional
Table 2
[tex]x_{1}[/tex] = 7 [tex]y_{1}[/tex] = 1
[tex]x_{2}[/tex] = 14 [tex]y_{2}[/tex] = 2
[tex]x_{3}[/tex] = 28 [tex]y_{3}[/tex] = 4
[tex]x_{4}[/tex] = 35 [tex]y_{4}[/tex] = 5
[tex]\frac{x_{1}}{y_{1}}[/tex] = 7/1 = 7
[tex]\frac{x_{2}}{y_{2}}[/tex] = 14/2 = 7
[tex]\frac{x_{3}}{y_{3}}[/tex] = 28/4 = 7
[tex]\frac{x_{4}}{y_{4}}[/tex]= 35/5 = 7
Since the ratio is the same throughout , it means that x and y are proportional.
Doing the same for table 3 and 4 , x and y are not proportional
