Question

In which table does y vary inversely with x?

Answer 1

Answer:

Table B

Step-by-step explanation:

Note that for y to vary inversely as x, an increase in x will cause a decrease in y. Therefore, by careful observation of tables A, B, C, and D, we would notice the following:

In table C:

As x increases from 1 to 2 to 3, y also increases from 26 to 52 to 78. Which means that an increase in x causes an increase in y. This is not an inverse variation.

In table D:

As x increases from 1 to 2 to 3, y also increases from -7 to -1 to 6. Which means that an increase in x causes an increase in y. This is also not an inverse variation.

We are left with options A and B

If y varies inversely as x, the following relationship must hold:

$y \alpha \frac{1}{x}\\y = \frac{k}{x}$

Where k is a constant of proportionality

considering option B:

When x = 1, y = 36

36 = k/1

k = 36 * 1

k = 36

when x = 2, y = 36/2

y = 18

when x = 3, y = 36/3

y = 12

These tally with all that is indicated in the table. Option B is an inverse variation