Question

Is the relationship between the variables in the table a direct variation, an inverse variation, both, or neither? If it is direct or inverse write a function to model it.
x 2 5 20 40
y 40 20 5 2

Answer 1

Answer:

Neither

Step-by-step explanation:

In direct variation, as one number increases, the other number also increases and as one number decreases, the other number also decreases. In inverse variation, as one number increases, the other number decreases and as as one number decreases, the other number increases.

For direct variation, $y=kx$ and for indirect variation, $y=\frac{k}{x}$ where k is a constant.

x  2    5   20  40

y  40  20  5     2

Here,

$\frac{2}{40}=\frac{1}{20}\\ \frac{5}{20}=\frac{1}{4}\\ \frac{20}{5}=4 \\\frac{40}{2} =20$

So, this is neither a direct variation nor an indirect variation.