Question

What is the direct linear variation equation for the relationship?

y varies directly with x and y=4 when x=12

A. y=
`(1)/(3)`x

B. y=3x

C. y=x+8

D. y=x-8

Answer 1

`\bf \begin{array}{cccccclllll} \textit{something}&&\textit{varies directly to}&&\textit{something else}\\ \quad \\ \textit{something}&=&{{ \textit{some value}}}&\cdot &\textit{something else}\\ \quad \\ y&=&{{ K}}&\cdot&x \\ \\ && y={{ K }}x \end{array} \\ \quad \\ \begin{cases} y=4\\ x=12 \end{cases}\implies y=Kx\implies 4=K\cdot 12`

solve for "K", to see what "K" is, or the "constant of variation",
once you found K, plug it back in y=Kx, and that's the equation