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

Accepted Solution

[tex]y=\frac{-6}{x}[/tex]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 [tex]y=kx[/tex] 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 [tex]y=\frac{k}{x}[/tex], where k is a constant of variation.  Let us find constant of variation using point (-2,3) for our given inversely proportional equation.[tex]3=\frac{k}{-2}[/tex]Multiplying both sides of our equation by -2 we will get,[tex]3*(-2)=\frac{k}{-2}*(-2)[/tex][tex]-6=k[/tex]      Therefore, the constant of variation is -6. Let us substitute [tex]-6=k[/tex] in inverse proportion to get our equation.[tex]y=\frac{-6}{x}[/tex]Therefore, the equation [tex]y=\frac{-6}{x}[/tex] represents the given relation in the graph.