Direct Variation: Suppose y varies directly with the square of x. If y is 81 when x is 3, find y when x is 2.

Question

Direct Variation

Answer 1

Hello, thank you for taking the time to post your question!

If y varies directly with the square of x that means that

y = k * x^2

if you plug in the given values we can solve for the value of k

81 = k * 3^2

81 = 9k

k = 81/9 = 9

meaning that when x = 2 the equation here will be

y = 9(2)^2 = 9(4) = 36

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

If y varies directly with the square of x, then we have:

 

y = kx²

 

81 = k(3)²

 

81 = 9k

 

k = 9 = the constant of variation

 

Now, let x = 2

 

y = 9(2)²

 

y = 9 * 4

 

y = 36