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

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 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 , where k is a constant of variation.  

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

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

Therefore, the constant of variation is -6.

Let us substitute in inverse proportion to get our equation.

Therefore, the equation represents the given relation in the graph.

the answer is y < -3 or   y > 3

-3y > 7 + 2

-3 y > 9

y < -3