Question

If y is 6 when x is 3 and y varies directly with x, find y when x is 8.

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Answer 1

Hey Katelyn :)
If y varies `directly` with x`, we can show this relationship as,\[\Large\rm y=kx\]
This problems requires us to find some constant of variation, \(\Large\rm k\), first.

Answer 2

We'll use the first set of information they gave us to figure out k.
When y=6, x=3,
\[\Large\rm 6=k\cdot3\]

Answer 3

What do you get for your k value? :)

Answer 4

3?

Answer 5

im not sure

Answer 6

Hmm so the 3 is `multiplying` the k.
To solve for k, we'll do the opposite.
We'll divide both sides by 3.

Answer 7

which is 2

Answer 8

\[\Large\rm \frac{6}{3}=k\]Ok good :)

Answer 9

We go back to our original equation, and plug the k in.\[\Large\rm y=kx\]\[\Large\rm y=2x\]

Answer 10

When x=8, what is your y?\[\Large\rm y=2\cdot8\]

Answer 11

16

Answer 12

Yayyy good job \c:/

Answer 13

yay!:) thank you!!