Question

y varies directly as x, and y = -1\4 when x = 8. a. Find constant of variation and b. Find y when x = 12. Please explain this to me as well as help me solve this

Answer 1

y varies directly as x

means that

y = kx

where k is some fixed number

Answer 2

we are told that "y = -1/4 when x = 8"

so

y = kx

-1/4 = k*8

solve for k

Answer 3

So then, divide -1\4 by 8?

Answer 4

to get k = ???

Answer 5

yes

Answer 6

yes but what do you get for k when you do that

Answer 7

-0.031

Answer 8

keep it as a fraction

Answer 9

so -31\100?

Answer 10

-1/4 = k*8

(-1/4)/8 = k

k = (-1/4)/8

k = (-1/4)*(1/8)

k = ??

Answer 11

um...-1 over 32?

Answer 12

That's what my textbook says the answer is

Answer 13

that is correct, k = -1/32

Answer 14

But when you take -1\4 divided by 1\8 you have to multiply -1\4 by 8 over 1 which ends up being 2, so how did they get -1\32?

Answer 15

no, when you divide -1/4 by 8, you are doing this

(-1/4)/8

(-1/4)*(1/8)

(-1*1)/(4*8)

-1/32

Answer 16

Or do you not multiply by the reciprocal of 1\8?

Answer 17

Oh I think I get it

Answer 18

because remember, when dividing fractions, you flip the second fraction and multiply

Answer 19

So for the second half of the question, you take -1\4 and multiply it by the opposite of 12?

Answer 20

what was k again

Answer 21

remember the general formula is

y = kx

Answer 22

Oh wait...k is -1\32, which means you take -1\4 = -1\32 times 12

Answer 23

no

Answer 24

y = kx

y = (-1/32)*x ... replace k with -1/32

now you plug in x = 12 to get

y = (-1/32)*12

y = ??

Answer 25

-3\8

Answer 26

yep, y = -3/8

btw it's not a big deal, but your fraction slashes are going the wrong way (just wanted to let you know)

Answer 27

So if s varies directly as the square of t and s and t both equal 10, would you use the inverse variation to solve it?

Answer 28

no it says directly

Answer 29

not inversely

Answer 30

So then, would be s = kt^2 which would turn it into 10 = k (10)^2 ?

Answer 31

good, now solve for k

Answer 32

keep it as a fraction

Answer 33

1\10 ?

Answer 34

1/10 yes, good

Answer 35

When I make 5 equal to t, I keep getting 2\5 when it should be 5\2...what am I doing wrong?

Answer 36

s = kt^2

s = (1/10)t^2

s = (1/10)(5)^2

s = (1/10)*25

s = 25/10

s = 5/2

Answer 37

not sure, but you somehow flipped things somewhere

Answer 38

I just did 10\1 instead of 1\10

Answer 39

ah, you have to keep k the same