Question

If y varies directly as x and y = 6 when x = 2, find y if x = 4. (Round off your answer to the nearest hundredth.)

Answer 1

We know that y varies directly with x to the power of 3, which means that we can express y as:

`y=kx^3`

where k is the constant of proportionality. To determine the value of k we plug y=6 and x=2 in the expression above and solve the resulting expression:

`\begin{gathered} 6=k(2)\placeholder{⬚}^3 \\ 8k=6 \\ k=(6)/(8) \\ k=(3)/(4) \end{gathered}`

Hence the value of k is 3/4 and the expression for y is:

`y=(3)/(4)x^3`

Plugging x=4 we have that:

`\begin{gathered} y=(3)/(4)(4)\placeholder{⬚}^3 \\ y=(3)/(4)(64) \\ y=48 \end{gathered}`

Therefore, when x=4 the value of y is 48.