Question

Is the relationship between the variables a direct variation, an inverse variation or neither? If there is a variation write the function rule, where x is 2,3,4,5 y = 9,6,4.5,3.6

Answer 1

Answer:

Indirect variation

Rule: $y = \frac{18}{x}$

Step-by-step explanation:

Given

$x \to 2,3,4,5$

$y \to 9,6,4.5,3.6$

Required

Determine the type of variation

For direct variation, we have:

y increases, as x increases

In the above function, y decreases, as x increases

Hence, it is not a direct variation

Indirect variation.

In an indirect variation, y decreases, as x increases

And the equation is given as:

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

Make k the subject

$k =xy$

Where k is the constant of variation.

For:

$(x,y) = (2,9)$

$k = 2 * 9 = 18$

For:

$(x,y) = (3,6)$

$k = 3 * 6 = 18$

For every other values;

$k = x * y = 18$

Hence, it is an indirect variation.

The rule is:

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

Substitute 18 for k

$y = \frac{18}{x}$