Question

If y varies directly as x, and y=42 as x=6, how do you find y for the x-value 3?

Answer 1

Direct variation can be represented as:
`x/y = k`
where `color(green)(k` is the constant

`x = 6 and y = 42`
so substituting :
`6/42 = k`
`color(green)(k = 1/7`

Now, we have the value of `color(green)(k)` and `x = 3` , substituting these in the variation to find `y`
`x/color(red)(y) = k`

`3/color(red)(y )= 1/7`

By cross multiplying we get
`color(red)(y = 21`

on observing the values

• when `x = 6 , color(red)(y) = color(green)(7)xx6= 42`
• when `x = 3 , color(red)(y) = color(green)(7)xx3 = 21`

`color(red)(y` is always `7` times `x` , as the constant `color(green)(k = 7`