Question

If y is directly proportional to x and y=5 when x=2, what is the value of y when x=16?

Answer 1

`y=40`

Explanation:

`ypropx`
`y=kx`

when `x=2`, `y=5`
`5=k(2)`
`:.k=5/2`

When `x=16`,
`y=(5/2)(16)`
`y=40`

Answer 2

`y=40`

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=5" when " x=2`

`y=kxrArrk=y/x=5/2`

`"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=5/2x=(5x)/2)color(white)(2/2)|)))`

`"when "x=16" then"`

`y=5/cancel(2)^1xxcancel(16)^8=5xx8=40`