Question

If f(x) varies directly with x and f(x) = 40 when x = 8, find the value of f(x) when x = 2.

Answer 1

For this case we have a direct variation of the form:

`f (x) = kx`

Where "k" is the constant of proportionality. To find it, we use the following data:

`f (x) = 40\ and\ x = 8`

Substituting:

`40 = k * 8`

Clearing the value of k:

`k = \frac {40} {8}\\k = 5`

Thus, the direct variation is given by:

`f (x) = 5x`

For
`x = 2` we have:

`f (2) = 5 * 2\\f (2) = 10`

Answer:

The value of the direct variation for
`x = 2`is:
`f (2) = 10`