Question

Can you please explain this to me?
If f(x) varies directly with x, and f(x) = 12 when x = 8, write the direct linear variation equation.
@MajicMuzyk @mathstudent55

Answer 1

We had a problem before that was
f(x) = 50x, remember?

Answer 2

yes I remember

Answer 3

so f(8)=12?

Answer 4

We found the constant of variation to be 50.

In general, y = mx, or f(x) = mx is a direct variation, and m is the constant of variation.
You may know m already as the slope.

Answer 5

right but then what?

Answer 6

If you have a direct variation problem, you know it's going to be

f(x) = mx

All you need to find now is what value m will have.

Answer 7

For that, you use the given point (8, 12)

Answer 8

Since you are told that when x = 8, f(x) = 12, that means f(8) = 12.

Answer 9

ok but that is that my answer? because shouldnt it be f(x)=12x or f(x)=8x

Answer 10

Now use the equation I gave you above, replace x with 8 and f(x) with 12, and solve for m.

\(f(8) = m \times 8= 12 \)

\(8m = 12\)

\(m = \dfrac{12}{8} \)

\(m = \dfrac{3}{2} \)

Answer 11

so then it turns into f(x)=3/2?

Answer 12

Almost. You need the x.

Now we know that m, the constant of variation is 3/2, we replace m with 3/2:

\(f(x) = \dfrac{3}{2}x\)

That is the final answer.

Answer 13

Oh my gosh thank you so much that was stressful! :)

Answer 14

To be sure, try to find f(8). It should be equal to 12:

\(f(x) = \dfrac{3}{2} x\)

\(f(8) = \dfrac{3}{2} \times 8 \)

\(f(8) = \dfrac{3}{2} \times \dfrac{8}{1} \)

\(f(8) = \dfrac{24}{2} \)

\(f(8) = 12\)

This shows the function is correct.

Answer 15

You are welcome.

Answer 16

ok wow that was a great help!!! thanks again! @mathstudent55