Question

If y varies directly as x and y=3 when x= 2, find y when x=8?

Answer 1

`y=12`

Explanation:

`"the initial statement is "ypropx`

`"to convert to an equation multiply by k the constant"`
`"of variation"`

`rArry=kx`

`"to find k use the given condition"`

`y=3" when "x=2`

`y=kxrArrk=y/x=3/2`

`"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=3/2x)color(white)(2/2)|)))`

`"when "x=8" then"`

`y=3/cancel(2)^1xxcancel(8)^4=3xx4=12`

Answer 2

`y =12` when `x = 8`

Explanation:

Given : `y` varies directly as `x`
`therefore x prop y`

`=> x = k y`, where `k` is constant of proportionality.

`=> y = x/k`--------(1)

When `x= 2, y = 3`

`=> 2 = k xx 3`

`=> k = 2/3`

`therefore` when x =8, (1) `=> y = 8/ (2/3)`

`=> y= 8 xx 3/2 = 4 xx 3 = 12`

`y =12`