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:

Where:

k: It is the constant of proportionality.

Then, we look for the value of "k":

So, now we look for the value of "y" when x = 20.

Thus, the value of y is 36

Final answer is y=36 and the constant of variation is k=9/5.

Step-by-step explanation:

Given that the variable y varies directly to the variable x.

Then we can write equation as y=kx

Were k is the constant of variation.

Given that If y = 9, then x = 5.

Plug these values into above equation, we get:

y=kx

9=5k

5k=9

k=9/5

Now we need to find the value of y when x = 20. So plug x = 20 and k=9/5 into above formula

y=kx

y=(9/5)(20)

y=180/5

y=36

Hence final answer is y=36 and the constant of variation is k=9/5.