Question

If y varies directly with x, write an equation for the direct variation. Then find each value.1. If x= -12 when y= -3 find x when y= -6

Answer 1

Since y varies directly with x then

`\begin{gathered} (y)/(x)=k \\ \text{Where k }is\text{ the constant of proportionality} \end{gathered}`

So,

`(y)/(x)=(-3)/(-12)=(3)/(12)=(1\cdot3)/(4\cdot3)=(1)/(4)`

Then, 1/4 is the constant of proportionality. So that,

`\begin{gathered} (y)/(x)=(1)/(4) \\ (-6)/(x)=(1)/(4) \\ -(6)/(x)\cdot x=(1)/(4)\cdot x \\ -6=(x)/(4) \\ 4\cdot-6=(x)/(4)\cdot4 \\ -24=x \end{gathered}`