Answer: Table #4
Step-by-step explanation:
We know that if two quantities x and y are proportional it mean their ratio is proportional.
i.e. [tex]\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}[/tex]
For table 1# x 3 4.5 8 12
y 2 3 4 8
Here , [tex]\dfrac{3}{2}=1.5[/tex]
[tex]\dfrac{3}{4.5}=0.67[/tex]
But 1.5 ≠0.67.
⇒ This table does not show a proportional relationship between x and y.
For table 2# x 1 4 5 10
y 15 60 70 120
Here , [tex]\dfrac{15}{1}=15[/tex]
[tex]\dfrac{60}{4}=15[/tex]
[tex]\dfrac{70}{5}=14[/tex]
But 14 ≠ 15
⇒ This table does not show a proportional relationship between x and y.
For table 3 # x 8 12 14 16
y 2 3 4 5
Here , [tex]\dfrac{2}{8}=0.25[/tex]
[tex]\dfrac{3}{12}=0.25[/tex]
[tex]\dfrac{4}{14}=0.286[/tex]
But 0.286 ≠ 0.25
⇒ This table does not show a proportional relationship between x and y.
For table 4# x 1 2 5 7
y 5 10 25 35
Here , [tex]\dfrac{5}{1}=5[/tex]
[tex]\dfrac{10}{2}=\dfrac{25}{5}=\dfrac{35}{7}=5[/tex]
⇒ This table shows a proportional relationship between x and y.
Hence, table #4 shows the a proportional relationship between x and y.
