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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
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
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
--- <em>Simplify fraction to lowest term by dividing by 5</em>
So, <em>when x = 15, y = 5.</em>
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
--- <em>Simplify fraction to lowest term by dividing by 2</em>
We can't conclude yet, if the constant of proportionality between y and x in table B is until we check further
When
The constant of proportionality becomes
--- <em>Convert to decimal</em>
<em>Simplify fraction to lowest term by dividing by 0.5</em>
-- 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
When x = 18, y = 3
The constant of proportionality becomes
--- <em>Simplify fraction to lowest term by dividing by 3</em>
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,
The constant of proportionality becomes
--- <em>Convert to fraction to decimal</em>
<em>Simplify fraction to lowest term by dividing by 4.5</em>
We still can't conclude until we check further
When x = 33,
The constant of proportionality becomes
--- <em>Convert to fraction to decimal</em>
<em>Simplify fraction to lowest term by dividing by 5.5</em>
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"