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*-6 \\ -30=-6k \\ \text{divide both sides by -6} \\ (-30)/(-6)=(-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*-4 \\ x=-20 \end{gathered}`

Hence, x is -20.