Question

Suppose y varies directly with x, and y=6 when x=-2. Find x when y=9

Answer 1

The fact that y varies directly with x means that they have a relation like:

`y=kx`

Where k can be any number. We know that y=6 when x=-2 which means that k is given by:

`\begin{gathered} y=kx \\ 6=-2k \\ (6)/(-2)=k \\ k=-3 \end{gathered}`

Then if y=9 we get:

`\begin{gathered} y=-3x \\ 9=-3x \\ (9)/(-3)=x \\ x=-3 \end{gathered}`

So x=-3 when y=9.