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Which table has a constant of proportionality between y and x of 1/6?
(choose 1 answer.)
A:
x--> 15 ---19
--- 36
y--> 5 ---- 6
---- 12
B:
x--> 12 ---13
--- 24
y--> 2 ---- 3
---- 14
C:
x--> 18 --- 27 --- 33
y--> 3 ---- 4
---- 5![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
Answer:
<em>Table C has 1/6 as the constant of proportionality between y and x</em>
Step-by-step explanation:
Given
Table A, B, C
Required
To check which of the tables has a constant of proportionality of 1/6
The constant of proportionality is calculated by dividing individual values of y column with x column.
Mathematically, this is represented by
![k = \frac{y}{x}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7By%7D%7Bx%7D)
Where k is the constant of proportionality
Recall Table A
x--> 15 ---19
--- 36
y--> 5 ---- 6
---- 12
When x = 15, y = 5.
The constant of proportionality becomes
![k = \frac{y}{x}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7By%7D%7Bx%7D)
--- <em>Simplify fraction to lowest term by dividing by 5</em>
![k = \frac{1}{3}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B1%7D%7B3%7D)
So, <em>when x = 15, y = 5.</em>
![k = \frac{1}{3}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B1%7D%7B3%7D)
is not equal to
; So, we do not need to check further in table A.
Hence, table A does not have <em>1/6 as the constant of proportionality between y and x</em>
<em />
We move to table B
Recall Table B
x--> 12 ---13
--- 24
y--> 2 ---- 3
---- 14
When x = 12, y = 2.
The constant of proportionality becomes
![k = \frac{y}{x}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7By%7D%7Bx%7D)
--- <em>Simplify fraction to lowest term by dividing by 2</em>
![k = \frac{1}{6}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B1%7D%7B6%7D)
We can't conclude yet, if the constant of proportionality between y and x in table B is
until we check further
When ![x = 3\frac{1}{2} , y = 13\frac{1}{2}](https://tex.z-dn.net/?f=x%20%3D%203%5Cfrac%7B1%7D%7B2%7D%20%2C%20y%20%3D%2013%5Cfrac%7B1%7D%7B2%7D)
The constant of proportionality becomes
![k = \frac{y}{x}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7By%7D%7Bx%7D)
--- <em>Convert to decimal</em>
<em>Simplify fraction to lowest term by dividing by 0.5</em>
![k = \frac{3.5/0.5}{13.5/0.5}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B3.5%2F0.5%7D%7B13.5%2F0.5%7D)
-- This cannot be simplified any further
is not equal to
; So, we do not need to check further in table B.
Hence, table B does not have <em>1/6 as the constant of proportionality between y and x</em>
<em />
We move to table C
Recall Table C
x--> 18 --- 27 --- 33
y--> 3 ---- 4
---- 5![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
When x = 18, y = 3
The constant of proportionality becomes
![k = \frac{y}{x}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7By%7D%7Bx%7D)
--- <em>Simplify fraction to lowest term by dividing by 3</em>
![k = \frac{1}{6}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B1%7D%7B6%7D)
We can't conclude yet, if the constant of proportionality between y and x in table C is
until we check further
When x = 27, ![y = 4\frac{1}{2}](https://tex.z-dn.net/?f=y%20%3D%204%5Cfrac%7B1%7D%7B2%7D)
The constant of proportionality becomes
![k = \frac{y}{x}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7By%7D%7Bx%7D)
--- <em>Convert to fraction to decimal</em>
<em>Simplify fraction to lowest term by dividing by 4.5</em>
![k = \frac{1}{6}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B1%7D%7B6%7D)
We still can't conclude until we check further
When x = 33, ![y = 5\frac{1}{2}](https://tex.z-dn.net/?f=y%20%3D%205%5Cfrac%7B1%7D%7B2%7D)
The constant of proportionality becomes
![k = \frac{y}{x}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7By%7D%7Bx%7D)
--- <em>Convert to fraction to decimal</em>
<em>Simplify fraction to lowest term by dividing by 5.5</em>
![k = \frac{1}{6}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B1%7D%7B6%7D)
Notice that; for every value of x and its corresponding value of y, the constant of proportionality, k maintains
as its value
Hence, we can conclude that "Table C has 1/6 as the constant of proportionality between y and x"