Question

Direct Variation Equations - If y = -8 when x = -2, find x when y = 32

Answer 1

So, the direct variation is:

\(\large\color{black}{ y=k~x}\) (where k is a constant.

plug in your numbers that you are given.
\(\large\color{black}{ -8=k~(-2)}\)

can you find the k ?

Answer 2

After you find the k, plug in the value of k, and 32 for y, into
\(\large\color{black}{ y=k~x}\), to solve for x.

Answer 3

Okay, so we have \(\large\color{black}{ y=kx }\). Do you understand what this means?

Answer 4

i think it is the formula for direct variation or something similar to that. I was absent when the teacher went over this lesson so i dont have any notes on this.

Answer 5

Okay, so lets start piece by piece.
You can see that a direct variation, \(\large\color{black}{ y=kx }\) , is similar to a line (with a slope of "k"), right?

Answer 6

kinda

Answer 7

I apologize, connection snapped.

Answer 8

that has been happening to me alot

Answer 9

there is one thing, here,
\(\large\color{black}{ y=kx }\) is a direct variation, but
\(\large\color{black}{ y=kx +b }\) (when \(\large\color{black}{ b \ne 0 }\) ) is NOT a direct variation.

Answer 10

okay

Answer 11

So, \(\large\color{black}{ y=kx }\) is a PROPORTIONAL relationship.
(and when taking about a line, it is a line that must be going through the origin, -- through (0,0) , because the y-intercept is 0)

Answer 12

But, lets see, what if we know thta
`y = -8 when x = -2`?

Answer 13

So, we can plug the y and the x, to find k.

Answer 14

\(\large\color{black}{ (-8)=k(-2) }\) see how I am plugging in?

Answer 15

yea

Answer 16

but my hw says find x when y = 32, so thats where i get confused

Answer 17

Okay, so we have,
\(\large\color{black}{ (-8)=k(-2) }\)
can tyou solve for k?

Answer 18

to solve for k, you have to eliminate it. How can you eliminate the "k" ?

Answer 19

I mean isolate, not eliminate.

Answer 20

eliminate it from both sides of the equation?

Answer 21

I meant isolate. sorry for that mistake.

Answer 22

oh okay isolate. you have to move the -2 to the other side with the 8

Answer 23

divide by -2 on both sides.

Answer 24

which would be 4 = k right?

Answer 25

\(\large\color{black}{ (-8)=k(-2) }\)
\(\large\color{black}{ (-8)\color{red}{\div (-2)}=k(-2)\color{red}{\div (-2)} }\)

Answer 26

yes, k=4.

Answer 27

So now that you know that k=4, you can write.
\(\large\color{black}{ y=\color{blue}{4}x }\)

Answer 28

and then you are asked to find x, when y=32.
So plug in 32 instead of y, into \(\large\color{black}{ y=\color{blue}{4}x }\)
and solve for x.

Answer 29

8?

Answer 30

yes, x is 8, when y=32.

Answer 31

So, lets do an overview okay?

Answer 32

oh okay i think i get it now

Answer 33

Your question
`Direct Variation Equations - If y = -8 when x = -2, find x when y = 32`

Solution:
\(\large\color{black}{ y=\color{blue}{k}x }\)
\(\large\color{black}{ (-8)=\color{blue}{k}(-2) }\)
\(\large\color{black}{ \color{blue}{k}=4 }\)

\(\large\color{black}{ y=\color{blue}{4}x }\)
\(\large\color{black}{ (32)=\color{blue}{4}x }\)
\(\large\color{black}{ x=8 }\)

Answer 34

Thanks, i understand this lesson now. Is there a way i can +1 your profile?

Answer 35

what do you mean to +1 my profile?

Answer 36

you want to view it?

Answer 37

on some websites you can increase or decrease someones reputation/rank so i was wondering if this website had something like that

Answer 38

Well, no really. You can fan write people a testimonial, or give them medals (and remove the given medals, or un-fan people, and delete the testimonials you write)
but you can't rate a user.

Answer 39

I mena not really.

Answer 40

ok, thanks again for helping me

Answer 41

Sure, not a problem:)