Question

Which table has a constant of proportionality between y and x of 1/6?

Answer 1

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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$\frac{1}{2}$ --- 36

y--> 5 ---- 6$\frac{1}{2}$ ---- 12

B:

x--> 12 ---13$\frac{1}{2}$ --- 24

y--> 2 ---- 3$\frac{1}{2}$ ---- 14

C:

x--> 18 --- 27 --- 33

y--> 3 ---- 4$\frac{1}{2}$ ---- 5$\frac{1}{2}$

Answer:

Table C has 1/6 as the constant of proportionality between y and x

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

$k = \frac{y}{x}$

Where k is the constant of proportionality

Recall Table A

x--> 15 ---19$\frac{1}{2}$ --- 36

y--> 5 ---- 6$\frac{1}{2}$ ---- 12

When x = 15, y = 5.

The constant of proportionality becomes

$k = \frac{y}{x}$

$k = \frac{5}{15}$ --- Simplify fraction to lowest term by dividing by 5

$k = \frac{1}{3}$

So, when x = 15, y = 5.

$k = \frac{1}{3}$

$\frac{1}{3}$ is not equal to $\frac{1}{6}$; So, we do not need to check further in table A.

Hence, table A does not have 1/6 as the constant of proportionality between y and x

We move to table B

Recall Table B

x--> 12 ---13$\frac{1}{2}$ --- 24

y--> 2 ---- 3$\frac{1}{2}$ ---- 14

When x = 12, y = 2.

The constant of proportionality becomes

$k = \frac{y}{x}$

$k = \frac{2}{12}$ --- Simplify fraction to lowest term by dividing by 2

$k = \frac{1}{6}$

We can't conclude yet, if the constant of proportionality between y and x in table B is $\frac{1}{6}$ until we check further

When $x = 3\frac{1}{2} , y = 13\frac{1}{2}$

The constant of proportionality becomes

$k = \frac{y}{x}$

$k = \frac{3\frac{1}{2}}{13\frac{1}{2}}$ --- Convert to decimal

$k = \frac{3.5}{13.5}$ Simplify fraction to lowest term by dividing by 0.5

$k = \frac{3.5/0.5}{13.5/0.5}$

$k = \frac{7}{27}$ -- This cannot be simplified any further

$\frac{7}{27}$ is not equal to $\frac{1}{6}$; So, we do not need to check further in table B.

Hence, table B does not have 1/6 as the constant of proportionality between y and x

We move to table C

Recall Table C

x--> 18 --- 27 --- 33

y--> 3 ---- 4$\frac{1}{2}$ ---- 5$\frac{1}{2}$

When x = 18, y = 3

The constant of proportionality becomes

$k = \frac{y}{x}$

$k = \frac{3}{18}$ --- Simplify fraction to lowest term by dividing by 3

$k = \frac{1}{6}$

We can't conclude yet, if the constant of proportionality between y and x in table C is $\frac{1}{6}$ until we check further

When x = 27, $y = 4\frac{1}{2}$

The constant of proportionality becomes

$k = \frac{y}{x}$

$k = \frac{4\frac{1}{2}}{27}$ --- Convert to fraction to decimal

$k = \frac{4.5}{27}$ Simplify fraction to lowest term by dividing by 4.5

$k = \frac{1}{6}$

We still can't conclude until we check further

When x = 33, $y = 5\frac{1}{2}$

The constant of proportionality becomes

$k = \frac{y}{x}$

$k = \frac{5\frac{1}{2}}{33}$ --- Convert to fraction to decimal

$k = \frac{5.5}{33}$ Simplify fraction to lowest term by dividing by 5.5

$k = \frac{1}{6}$

Notice that; for every value of x and its corresponding value of y, the constant of proportionality, k maintains $\frac{1}{6}$ as its value

Hence, we can conclude that "Table C has 1/6 as the constant of proportionality between y and x"