Question

I understand what direct variation is but now I need help solving a different question and im confused again...



Which equations show a direct variation between x and y when solved for y?

Choose all answers that are correct.

A. y-9=2x+9


B. y=4/7x


C. 4+y=1/3x+4


D. y=3/x

Answer 1

@jim_thompson5910

Answer 2

let's focus on y-9=2x+9 for now

Answer 3

how would you isolate y?

Answer 4

+9 and cancel it out?

Answer 5

yes add 9 to both sides

Answer 6

y-9=2x+9

y-9+9=2x+9+9

y = 2x + 18

Answer 7

so y=2x+18

Answer 8

oh you already put it lol

Answer 9

that's ok. So is y = 2x+18 in the form y = k*x ?

Answer 10

I think if there's no 18, then yes

Answer 11

so because of that added 18, it means it's not in direct variation form

Answer 12

So A can't be one of the answers

Answer 13

agreed

Answer 14

if choice B is \[\Large y = \frac{4}{7}x\] then is it in y = k*x form?

Answer 15

Yes

Answer 16

good, so k = 4/7 in this case

Answer 17

And for C, i'll try to do the same thing we did for A.

Answer 18

yes

Answer 19

what do you get?

Answer 20

Cancel out the 4 on both sides and you get y=1/3x which is in the form of y=k*x, right?

Answer 21

yep k = 1/3 here

Answer 22

So what about D?

Answer 23

D is in the form y = k/x where k = 3 in this case. This is inverse variation (not direct variation)

Answer 24

Oh like the other one we did earlier, so D isn't an option... so the answers are A and C

Answer 25

*B and C

Answer 26

yes B and C are the two answers

Answer 27

so the next question is asking for the constant of variation, how do I find that?

Answer 28

it's the value being multiplied by the x

example: y = 3x has a constant of variation of k = 3

Answer 29

There's a table involved...

https://static.k12.com/calms_media/media/240500_241000/240875/1/84c7a8e958278f581d334091e36c5623014c9a18/01_09_LQ_2.gif

Answer 30

focus on the column with x = 1 and y = 3


y = k*x

3 = k*1 ... replace x with 1 and y with 3


solve for k

Answer 31

1?

Answer 32

3 is equal to SOMETHING times 1

what is that SOMETHING?

Answer 33

1/3?

Answer 34

3 = k*1
so k = 3

Answer 35

k = 3 is the constant of variation

Answer 36

Ohh It's 3 for the rest of them too if you solve them the same way

Answer 37

yeah notice how if x = 2 then y = 6. You'd get the same value of k