Question

If y is directly proportional to x² and y=2 when x=3 Find the value of y when x=6
Please Help

Answer 1

y = 8

Explanation:

Given that y is directly proportional to x² then the equation relating them is

y = kx² ← k is the constant of variation

To find k use the condition y = 2 when x = 3, then

2 = k × 3² = 9k ( divide both sides by 9 )

`(2)/(9)` = k

y =
`(2)/(9)` x² ← equation of proportion

When x = 6, then

y =
`(2)/(9)` × 6² =
`(2)/(9)` × 36 = 2 × 4 = 8