Determine whether y varies directly with x. If so, find the constant of variation and write the function rule.y183642214422Does y vary directly with x?No♥ YesWhat is the constant of variation? Select the correct choice and fill in any answer boxes in your choice below.O A. k=| (Simplify your answer. Type an integer or a fraction.)O B. There is no constant of variation.PrintHelp me solve thisaO Type here to search

The given data is X= 36,42,44 Y= 18,21,22 It is required to determine whether y varies directly with x and find the constant of variation and the function rule.It is known that direct variation describes a relationship between two variables.If y varies directly with x, y=kx Where k is called the constant of variation or constant of proportionality. That is, when x increases y increases and as x decreases y decreases and the ratio between them always remains the same. From the given set of values note that as x increases y increases. Now substitute 36 for x and 18 for y in y=kx. y=kx18=k×36k=1836k=12 Also substitute 42 for x and 21 for y in y=kx. y=kx21=k×42k=2142k=12 Now substitute 44 for x and 22 for y in y=kx. y=kx22=k×44k=2244k=12 Since the ratio between the given set of values always remains the same. Therefore, the variation is a direct variation and y varies directly with x. Therefore, the constant of variation k is 12. Substitute 12 for k in y=kx. y=kxy=12x Thus, the function rule is given by y=12x.