Question

determine whether y varies directly with x. If so, find the constant of variation and write the equation. yes; k=4 and y=4xyes; k = -4 and y= -4xyes; k = -4 and x= -4yno(please help me)

Answer 1

Given the information on the table, we can find out the constant of variation by working a few cases:

`\begin{gathered} k=(y)/(x) \\ \Rightarrow k_1=(-8)/(-2)=4 \\ k_2=(-16)/(-4)=4 \\ k_3=(-24)/(-6)=4 \end{gathered}`

Therefore, k=4. To find the equation we simply solve for y the first equation:

`\begin{gathered} k=(y)/(x) \\ k=4 \\ \Rightarrow4=(y)/(x) \\ \Rightarrow4x=y \end{gathered}`

Finally, the equation is y=4x