Question

**GIVING MEDAL + FAN**

Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.

Answer 1

@pitamar
@lizzylou169
Please help ;-;

Answer 2

so, you got this one? i see it's closed

Answer 3

No I didn't get it :/ I just ran out of time, but I can still answer it! :D

Answer 4

Please help. Lol

Answer 5

Ok, you see on the left a list of x values, what's the differences between them?

Answer 6

what are* =|

Answer 7

When, they all increase by one? (7, 8, 9, 10)

Answer 8

I feel like that wasn't the answer to your question however.

Answer 9

yes, and the y values increase by how much?

Answer 10

By 2.

Answer 11

ok how would you write a simple function that makes y grow by 2 for every increase of 1 in the x?

Answer 12

It wouldn't be this one, but it's a start =]

Answer 13

uuuhmm....
y+2 > 1x

I don't know, I'm really bad at these :/

Answer 14

\[ y = 2x \]
since every x you add, adds 2 to the y

Answer 15

therefore if x = 1... 2*1 = 2. if x = 2... 2 * 2 = 4... so on. right?

Answer 16

Oh, I see! yes.

Answer 17

ok, this isn't exacly the function to those values though. let's see why. calculate f(7)

Answer 18

What's f...? multiply 7 by what?

Answer 19

\[ f(x) = 2x \]
wrote it as
\[y = 2x \]
before.. hehe

Answer 20

so 2x(7) then? o.o

Answer 21

f(7) means x = 7. and by
\[ f(x) = 2x \]
that means...

Answer 22

OH!

Answer 23

yes. so f(7) is what?

Answer 24

14x?

Answer 25

God, I know I'm wrong.

Answer 26

just 14 hehe
it's like saying
\[
y = 2x \\
x = 7 \\
y = 2 \cdot 7 = 14
\]

Answer 27

Oh, So I was sort-of getting it :D

Answer 28

ye but 14x and 14 are different things, and it could get you in alot of troubles. so make sure to understand it all.

Answer 29

what is f(9) for example?

Answer 30

f(9) = 18?
Just 18. No x :D

Answer 31

ye, ok

Answer 32

ok, so now we know how to make a function that increases by 2 for each increase of 1 on the x.
but they tell you that their function, let's call it g(x) for now has the following value
\[
g(7) = 11 \\
g(8) = 13 \\
g(9) = 15
\]

Answer 33

right?

Answer 34

yes, right.

Answer 35

calculate your f(7), f(8), f(9), and compare. what's the difference in all cases from the matching g(x)?

Answer 36

f(7) = 14
f(8) = 16
f(9) = 18

Sorry, but what do you mean by matching g(x)? Because if it's how much (basically) "14 *f(7)* is away from 11*g(7)*." then it would be 3.

Answer 37

ye basically. it seems by all those values that
\[ f(x) - g(x) = 3 \\
f(7) - g(7) = 14 - 11 = 3 \\
f(8) - g(8) = 16 - 13 = 3
\]
...

Answer 38

so that means we have to subtract 3 from every value on our f(x) to get g(x).. right?

Answer 39

right!

Answer 40

so let's make a new function... which would be f(x) - 3. let's call it h(x). remember, what f(x) really is? now try and write it

Answer 41

you know what let's keep it simple..
\[
f(x) - g(x) = 3 \\
f(x) - 3 = g(x)
\]

Answer 42

so would it be h(-3)?

Answer 43

since you know what f(x) ןד, what is g(x) in here?

Answer 44

or h(7, 8, 9)

Answer 45

forget about h(x). i was over complicating it.
\[ f(x) - g(x) = 3 \\
f(x) - 3 = g(x) \]
you know what f(x) really is. so find g(x) =] just simple replacing

Answer 46

to remind you
\[
f(x) = 2x
\]

Answer 47

(Sorry, Im juggling 2 question at one time. no prob)

so would g(x) = 3x?

Answer 48

or -3x?

Answer 49

once again.
\[ f(x) - g(x) = 3 \\
f(x) - 3 = g(x) \]
you know the definition of f(x). use it and get g(x)

Answer 50

Well, all I can think of is f(3) x 2x = 6...so g(6).

Answer 51

you're too confused. forget everything in your mind and follow me =]

Answer 52

Alright :D

Answer 53

we know that in order to make the value increase by 2 for each 1 x we define the following
\[
y = 2x \\
f(x) = 2x
\]
both are pretty much the same... just second one is a function that could get a value and be in thie case
\[
f(value) = 2 \cdot value
\]
that's the point of 'x' in there.
now. we know that
\[
f(7) - g(7) = 3 \\
f(8) - g(8) = 3\\
f(x) - g(x) = 3 \\
f(x) - 3 = g(x)
\]
since f(x) = 2x..
\[
g(x) = f(x) - 3 = 2x - 3 \\
g(x) = 2x - 3
\]

Answer 54

g(x)=2x−3 subtracting?
It wouldn't be g(-1), would it?

Answer 55

nonono.... it's not 2 - 3... it's 2x - 3.. and you leave it that way, because you have no idea what 'x' is..
that's the point. if it's g(5) then
\[
g(5) = 2 \cdot 5 - 3 = 10 - 3 = 7 \\
g(8) = 2 \cdot 8 - 3 = 16 - 3 = 13 \\
g(x) = 2 \cdot x - 3
\]

Answer 56

Oh I see! it was a formula! psh, i knew that ;D
So then for 15 (the next one) it would be g(9) = 2 x 9 - 3 = 15? :D

Answer 57

ye. =]

Answer 58

well, I guess that's it hehe, good luck with next one i guess

Answer 59

Thank you so much! I really needed help with that one. *whew*