Question

Which does not show a direct variation between x and y?

    A. y = x/9

   B. y = 2x    C. y = 0.5x    D. y = 9/x

If f(x) varies directly with x, and f(x) = 8 when x = 6, write the direct linear variation equation.  
 A.   f(x) = 3/4x    B. f(x) = 6x    C. f(x) = 8x    D. f(x) = 4/3 x

Find the constant of variation for the relationship f(x)= 30x.    A. 10    B. 30    C. x    D. f(x)


If f(x) varies directly with x, and f(x) = 56 when x = 8, find the value of f(x) when x = 2    A. 4    B. 7    C. 8    D. 14

Answer 1

`(1)\\direct\ variation\ between\ x\ and\ y:\ \ \ y=k\cdot x\ \ \ and\ \ \ k\in\ R\\\\Ans.\ NOT\ direct\ is\ D\\\\(2)\\f(x) = m\cdot x\ \ \ and\ \ \ f(6)=8\\\\ \Rightarrow\ \ \ m\cdot 6=8\ \ \ \Rightarrow\ \ \ m= (8)/(6) = (4)/(3) \ \ \ \ \Rightarrow\ \ \ \ Ans.\ D\\\\(3)\\f(x)=30x\ \ \ \Leftrightarrow\ \ \ (f(x))/(x) =30\ \ \ \ \ \ \Rightarrow\ \ \ \ constans=30\ \ \ \ Ans.\ B.`


`\\\\(4)\\f(x)=m\cdot x\ \ and\ \ f(8)=56\\\\m\cdot8=56\ \ \Leftrightarrow\ \ m= (56)/(8) =7\ \ \Rightarrow\ \ \ f(x)=7x\ \ \ \Rightarrow\ \ \ f(2)=7\cdot2=14\\\\Ans.\ D.`