The f(x)varies directly with x, and f(x)=8 when x=6
Which answer is the direct linear variation equation?
F (x) = 3/4x
F (x)= 8 my choice
F (×)=6x
F (×)= 4/3×
no, you picked a constant function. It is always 8.
Direct variation means that y = kx
for some constant k.
Since y(6)=8,
8 = k*6
k = 8/6 = 4/3
hence, f(x) = 4/3 x
choice D
To determine the equation that represents the direct variation between f(x) and x, we need to find the constant of variation, often denoted as k.
In a direct variation, the equation is of the form f(x) = kx, where k is the constant of variation. To find k, we can use the given information that f(x) = 8 when x = 6.
Substituting these values into the equation, we get:
8 = k * 6
To solve for k, we divide both sides of the equation by 6:
8/6 = k
Simplifying:
4/3 = k
Hence, the equation that represents the direct variation is f(x) = (4/3)x.