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),

$\begin{gathered} x\propto y \\ x=ky \\ k=\frac{x}{y} \end{gathered}$

For (x₁, y₁) = (3, 12),

$\begin{gathered} k=\frac{3}{12} \\ k=0.25 \end{gathered}$

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

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

Substituting,

$\begin{gathered} n=0.25\times8 \\ n=2 \end{gathered}$

Therefore, the value of n is 2