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: $f (2) = 10$