Question

Determine whether y varies directly with x. If so, find the constant of variation and write the equation.

Answer 1

`y=(-6)/(x)`

Constant of variation = -6.

Step-by-step explanation:

We have been given a graph and we are asked to determine whether y varies directly with x.

Since we know that directly variation means that when x increases, y increases by the same factor and equation
`y=kx` represents the relation between direct variation, where is k is constant of variation.

We can see from our given graph that as x is increasing y is decreasing, therefore, y does not vary directly with x.

As y decreases when x increases, so y varies inversely with x and the equation of inverse variation is of the form
`y=(k)/(x)`, where k is a constant of variation.

Let us find constant of variation using point (-2,3) for our given inversely proportional equation.

`3=(k)/(-2)`

Multiplying both sides of our equation by -2 we will get,

`3*(-2)=(k)/(-2)*(-2)`

`-6=k`

Therefore, the constant of variation is -6.

Let us substitute
`-6=k` in inverse proportion to get our equation.

`y=(-6)/(x)`

Therefore, the equation
`y=(-6)/(x)` represents the given relation in the graph.