Question

Can someone explain direct variation to me? I kind of don't understand the vocab; like constant of variation, etc. Thanks! xx

Answer 1

direct variation is the idea that if one variable goes up, then another variable goes up

put another way, as one variable increases, so does another

if one variable decreases, then the other variable decreases


what's important about direct variation equations is that they are always of the form

y = kx

where k is the constant of variation

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example: the equation y = 2x is a direct variation equation because as x increases, y increases. As x decreases, y decreases

Answer 2

I like to remember it as "direct as in what goes up directly affects the other to go up as well"

contrast this with "inverse variation" where if one goes up, the other goes down (or vice versa)

Answer 3

So the constant of variation is kind of like the rate it goes up? For every 1k there is 2k- so the rate is 2?

Answer 4

2x*

Answer 5

yes exactly, it's basically how fast one increases as you increase the other

Answer 6

Thank you!

Answer 7

Oh can you give me an example? Like step by step?

Answer 8

of a direct variation equation?

Answer 9

or inverse?

Answer 10

Both?

Answer 11

examples

direct: y = 7x

inverse: y = 62/x

did you need me to explain anything about them?

Answer 12

Here's an example from my homework: y varies directly to x. Find the constant of variation and write the equation of direct variation that relates the two variables.
y=-6/7 when x=-18/35

Answer 13

"y varies directly to x."

what does that mean in terms of an equation?

Answer 14

does it mean that y = k/x? or that y = kx?

Answer 15

y=kx

Answer 16

good

Answer 17

so if y = kx and y=-6/7 when x=-18/35, then how can we find k?

Answer 18

k=y/x?

Answer 19

how about replacing x and y with the values they give us then solve for k?

Answer 20

y = kx

-18/35 = k*(-6/7)

now solve for k

Answer 21

But how can I divide a fraction with a fraction? I don't get it -__-

Answer 22

Dividing a fraction: -18/35 divided by -6/7 is the same thing as multiplied by the reciprocal of -6/7, which is -7/6. multiply the numerators and the denominators to multiply the fractions.

Answer 23

Also, since we have 2 negatives, the answer is positive.

Answer 24

Can you do that step by step?

Answer 25

OK.

Answer 26

\[\frac{ 18 }{ 35 } * \frac{ 7 }{ 6 }\]

Answer 27

multiply 18 by 7
multiply 35 by 6

Answer 28

so, 126/210.

Answer 29

isn't it -7?

Answer 30

Yes, but we can cancel the negative signs b/c we're multiplying a negative by a negative, which will yield a positive no matter what.

Answer 31

Oh. Okay so then what does all of that mean? So 126/210 is k?

Answer 32

Yes. Simplify 126/210, though. (Divide num. and denom. by 2: 63/105)

Answer 33

Ugh. Okay, that's so complicated >.< Thanks!

Answer 34

haha. Yeah, a lot of math is complicated.

Answer 35

you need to reduce further

63/105 can be reduced further

Answer 36

by 3

Answer 37

divide both by 7 to reduce

Answer 38

right.

Answer 39

or 7. sorry.

Answer 40

Can you simplify it completely?

Answer 41

Also, I have another question about point slope form! What if I get this answer? 2x+1y=14 I can't have fractions, but x has to be one

Answer 42

you cant have fractions in standard form. point slope form is fine with it.

Answer 43

What if I have to put it in standard form?

Answer 44

Then 2x+y=14 is in standard form.

Answer 45

And no fractions.

Answer 46

And x is positive. So it's fine.

Answer 47

Do you understand?

Answer 48

Oh that's right! I thought for a second that x had to be one but it doesn't, it only has to be positive(:

Answer 49

Yup. Any other questions?

Answer 50

Nope(: Gheez you're good

Answer 51

I'm gonna have another question on literal equations soon, so heads up xD

Answer 52

OK :)