What that the fractions in this pattern have in common is that they are all the equivalent of $\displaystyle \frac{2}{3}$. 

The value of y should be a number that is the equivalent of $\displaystyle \frac{2}{3}$ when divided by 12. 

Given that $\displaystyle \frac{1}{3}$ of 12 is 4, $\displaystyle \frac{2}{3}$ of 12 would be equal to 8, the correct answer. 

In this sequence, every subsequent number is equal to one third of the preceding number:

$\displaystyle 108, 36, 12, 3, x$

$\displaystyle 108\div3=36$

$\displaystyle 36\div3=12$

$\displaystyle 12\div3=4$

Given that $\displaystyle 4\div3 =\frac{4}{3}$, that is the correct answer. 

In this set, each subsequent fraction is half the size of the preceding fraction; (the denominator is doubled for each successive fraction, but the numerator stays the same). Given that the last fraction in the set is $\displaystyle \frac{1}{16}$, it follows that the subsequent fraction will be $\displaystyle \frac{1}{32}$. 

In order to solve this question, we need to use both the equation and the table. We are looking for the corresponding $\displaystyle y$ value for $\displaystyle x=4$. We can plug $\displaystyle 4$ into the $\displaystyle x$ in our equation to solve for $\displaystyle y$.

$\displaystyle y=3(4)+6$

$\displaystyle y=12+6$

$\displaystyle y=18$

In order to solve this question, we need to use both the equation and the table. We are looking for the corresponding $\displaystyle y$ value for $\displaystyle x=5$. We can plug $\displaystyle 5$ into the $\displaystyle x$ in our equation to solve for $\displaystyle y$.

$\displaystyle y=4(5)+2$

$\displaystyle y=20+2$

$\displaystyle y=22$

In order to solve this question, we need to use both the equation and the table. We are looking for the corresponding $\displaystyle y$ value for $\displaystyle x=6$. We can plug $\displaystyle 6$ into the $\displaystyle x$ in our equation to solve for $\displaystyle y$.

$\displaystyle y=5(6)+7$

$\displaystyle y=30+7$

$\displaystyle y=37$

In order to solve this question, we need to use both the equation and the table. We are looking for the corresponding $\displaystyle y$ value for $\displaystyle x=13$. We can plug $\displaystyle 13$ into the $\displaystyle x$ in our equation to solve for $\displaystyle y$.

$\displaystyle y=6(13)+11$

$\displaystyle y=78+11$

$\displaystyle y=89$

In order to solve this question, we need to use both the equation and the table. We are looking for the corresponding $\displaystyle y$ value for $\displaystyle x=5$. We can plug $\displaystyle 5$ into the $\displaystyle x$ in our equation to solve for $\displaystyle y$.

$\displaystyle y=8(5)+12$

$\displaystyle y=40+12$

$\displaystyle y=52$

In order to solve this question, we need to use both the equation and the table. We are looking for the corresponding $\displaystyle y$$\displaystyle x=5$ value for . We can plug $\displaystyle 5$ into the $\displaystyle x$ in our equation to solve for $\displaystyle y$.

$\displaystyle y=9(5)+10$

$\displaystyle y=45+10$

$\displaystyle y=55$

In order to solve this question, we need to use both the equation and the table. We are looking for the corresponding $\displaystyle y$ value for $\displaystyle x=16$. We can plug $\displaystyle 16$ into the $\displaystyle x$ in our equation to solve for $\displaystyle y$.

$\displaystyle y=10(16)+4$

$\displaystyle y=160+4$

$\displaystyle y=164$