Question

f(x) varies directly with x and y=-2 when x=8
A.find the constant of variation k
B.write the direct variation equation
C.find the value of f(x) when x=-4
D.find the value of x when f(x)=4
@ranga

Answer 1

This is similar to the problem we did earlier.
y = k * x. when x = 8, y = -2. Solve for k.

Answer 2

-2=k*8

Answer 3

yes. so what is k?

Answer 4

then it turns into k=-2*8 right?

Answer 5

no. to solve for k you need to isolate k which can be done by dividing both sides by 8 and simplifying.

Answer 6

-0.25=k?

Answer 7

Leave it as a fraction instead of decimals.

Answer 8

so -1/4?

Answer 9

yes. a) k = -1/4

Answer 10

ok part b now.

Answer 11

y=k*x?

Answer 12

Yes. But you already solved for k and so put k = -1/4

Answer 13

but the part b says I have to write the direct variation equation that is the equation right?

Answer 14

y is same as f(x). So you can write it as f(x) = -1/4x (I use * so people don't think it is 1 divide by 4x. But when answering you don't have to use *).
I will use the math editor to show the answer properly:

Answer 15

\[f(x) = -\frac{ 1 }{ 4 }x\]

Answer 16

oh ok makes better sense ready to tackle part c?

Answer 17

C. Put x = -4 in the equation we got for B and find f(x).

Answer 18

f(4)=-1/4x?

Answer 19

We need to find f(-4)
f(x) = -1/4 * x
f(-4) = -1/4 * (-4) = 1

Answer 20

For D. Put f(x) = 4 into the equation and solve for x
f(x) = -1/4 * x
4 = -1/4 * x
multiply both sides by 4
16 = -x
x = -16

Answer 21

Ok thanks I lost my internet for a little bit but thanks for everything I greatly appreciate it! :)

Answer 22

@ranga

Answer 23

you are welcome.