For this case we have a direct variation of the form:
[tex]f (x) = kx[/tex]
Where "k" is the constant of proportionality. To find it, we use the following data:
[tex]f (x) = 40\ and\ x = 8[/tex]
Substituting:
[tex]40 = k * 8[/tex]
Clearing the value of k:
[tex]k = \frac {40} {8}\\k = 5[/tex]
Thus, the direct variation is given by:
[tex]f (x) = 5x[/tex]
For[tex]x = 2[/tex] we have:
[tex]f (2) = 5 * 2\\f (2) = 10[/tex]
Answer:
The value of the direct variation for [tex]x = 2[/tex]is: [tex]f (2) = 10[/tex]
