Question

What is the direct variation equation if f(x) varies directly with x and f(x) = -9 when x = 3?

a) f(x) = -6x
b) f(x) = -13x
c) f(x) = -3x
d) f(x) = -12x

Answer 1

The direct variation equation when f(x) varies directly with x and f(x) = -9 when x = 3 is f(x) = -3x. We determine this by calculating the constant of variation k, which is -3.

Step-by-step explanation:

To find the direct variation equation of f(x), we need to use the definition that f(x) varies directly with x. This means that f(x) = kx, where k is the constant of variation. We know that f(x) = -9 when x = 3, so we can substitute these values into the equation to find k.

f(3) = k * 3<r />
-9 = k * 3<r />
k = -9 / 3<r />
k = -3

Now that we have found k, we can write the direct variation equation as f(x) = -3x. So, the correct answer is c) f(x) = -3x.