Question

If x varies directly as y, and x=-30 when y=-6, find x when y=-4.

Answer 1

$x\text{ }\propto\text{ y}$

Let us now introduce a constant 'k' inorder to get the relationship between x and y,

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

Let us substitute x = -30 and y = -6 inorder to get the relationship,

$\begin{gathered} -30=k\times-6 \\ -30=-6k \\ \text{divide both sides by -6} \\ \frac{-30}{-6}=\frac{-6k}{-6} \end{gathered}$$\begin{gathered} k=5 \\ \text{The relationshiop betw}een\text{ x and y is,} \\ x=5y \end{gathered}$

Let us now solve for x when y = -4,

$\begin{gathered} x=5y \\ x=5\times-4 \\ x=-20 \end{gathered}$

Hence, x is -20.