Question

For each equation, determine whether it shows a direct variation (that is, shows directly proportional variables).If it does, find the constant of variation and write it in simplest form.-Click on Picture for the questions! More understandable-

Answer 1

(a) 2y=8x

`\begin{gathered} 2y=8x \\ y=(8x)/(2) \\ y=4x\Rightarrow y=kx\Rightarrow y\propto x\text{ \lbrack}direct\text{ }variation] \\ k=4 \end{gathered}`

(b) 7x=-2y-7 [ not direct variation ]

`\begin{gathered} 7x=-2y-7 \\ 7x+7=-2y \\ 7(x+1)=-2y \\ (x+1)=(-2y)/(7) \\ x=(-2y)/(7)-1 \end{gathered}`

We couldn't express in the form x=ky , hence variation is not direct. OR we can say we couldn't express in the form y=kx ....hence variation is not direct