Question

A direct variation includes the points (3, 12) and (n, 8). Find n.

Answer 1

For a direct variation between each point (x, y),

`\begin{gathered} x\propto y \\ x=ky \\ k=(x)/(y) \end{gathered}`

For (x₁, y₁) = (3, 12),

`\begin{gathered} k=(3)/(12) \\ k=0.25 \end{gathered}`

To find n, consider (n, 8) = (x, y)

`\begin{gathered} x=ky \\ \end{gathered}`

Substituting,

`\begin{gathered} n=0.25*8 \\ n=2 \end{gathered}`

Therefore, the value of n is 2