Question

If y varies directly with x, if y = 36 when x = -6, how do you find x when y = 54?

Answer 1

`x= -9`

Explanation:

Let `k` be a constant

Breaking down the question into parts:

If `y` varies directly with `x : -> y=kx........................(1)`
if `y=36` when `x=-6->36=kxx(-6) ..........(2)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("To find the value of "k)`

Consider equation (1)

`color(brown)(y=kx)`

Divide both sides by `x`. This is the same as `color(blue)(xx1/x)`

`color(brown)(ycolor(blue)(xx1/x)=kxcolor(blue)(xx1/x))`

`y/x=kxx x/x`

But `x/x=1` giving:

`k=y/x ........................................(3)`

Substitute values from (2) into equation (3) giving

`color(blue)(k=36/(-6) =-6)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("To find the value of "x" when "y=54)`

Using equation (1)

`y=kx-> 54=-6 x`

`color(blue)(=>x=54/(-6) = -9)`