Answer:
[tex]f(x)=6x[/tex] is a direct variation.
Step-by-step explanation:
Given the function
[tex]f(x)=6x[/tex]
We have to determine whether the equation [tex]y=6x[/tex] is a direct variation or not.
As we know that in direction variation, y and x increase or decrease by the same factor by the formula
[tex]y=kx[/tex]
where 'k' is the constant of variation
Given the function
[tex]y=6x[/tex]
Here 6 is the constant of variation ∵ [tex]y=kx[/tex]
Also y and x increase and decrease by the same factor
For example,
when x=6, y = 6(x)=6(6)=36
when x=8, y = 6(x) = 6(8) = 48
Hence, when x increase, the y increases by the same factor.
Therefore, [tex]f(x)=6x[/tex] is a direct variation.
