The variable y varies directly to the variable x. If y = 9, when x = 5, what is the value of y when x = 20? Show your work to find the constant of variation (k) Write the equation using the constant of variation (k).Show your work to find the value of y when x = 20.

For this case we have that if "and" varies directly proportional to "x", it follows that:[tex]y = kx[/tex]Where:k: It is the constant of proportionality.Then, we look for the value of "k":[tex]9 = k (5)\\k = \frac {9} {5}[/tex]So, now we look for the value of "y" when x = 20.[tex]y = \frac {9} {5} (20)\\y = \frac {180} {5}\\y = 36[/tex]Thus, the value of y is 36Answer:[tex]y = 36[/tex]