anonymous
  • anonymous
Can someone explain direct variation to me? I kind of don't understand the vocab; like constant of variation, etc. Thanks! xx
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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jim_thompson5910
  • jim_thompson5910
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 ------------------------------------------------------------------- example: the equation y = 2x is a direct variation equation because as x increases, y increases. As x decreases, y decreases
jim_thompson5910
  • jim_thompson5910
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)
anonymous
  • anonymous
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?

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anonymous
  • anonymous
2x*
jim_thompson5910
  • jim_thompson5910
yes exactly, it's basically how fast one increases as you increase the other
anonymous
  • anonymous
Thank you!
anonymous
  • anonymous
Oh can you give me an example? Like step by step?
jim_thompson5910
  • jim_thompson5910
of a direct variation equation?
jim_thompson5910
  • jim_thompson5910
or inverse?
anonymous
  • anonymous
Both?
jim_thompson5910
  • jim_thompson5910
examples direct: y = 7x inverse: y = 62/x did you need me to explain anything about them?
anonymous
  • anonymous
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
jim_thompson5910
  • jim_thompson5910
"y varies directly to x." what does that mean in terms of an equation?
jim_thompson5910
  • jim_thompson5910
does it mean that y = k/x? or that y = kx?
anonymous
  • anonymous
y=kx
jim_thompson5910
  • jim_thompson5910
good
jim_thompson5910
  • jim_thompson5910
so if y = kx and y=-6/7 when x=-18/35, then how can we find k?
anonymous
  • anonymous
k=y/x?
jim_thompson5910
  • jim_thompson5910
how about replacing x and y with the values they give us then solve for k?
jim_thompson5910
  • jim_thompson5910
y = kx -18/35 = k*(-6/7) now solve for k
anonymous
  • anonymous
But how can I divide a fraction with a fraction? I don't get it -__-
anonymous
  • anonymous
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.
anonymous
  • anonymous
Also, since we have 2 negatives, the answer is positive.
anonymous
  • anonymous
Can you do that step by step?
anonymous
  • anonymous
OK.
anonymous
  • anonymous
\[\frac{ 18 }{ 35 } * \frac{ 7 }{ 6 }\]
anonymous
  • anonymous
multiply 18 by 7 multiply 35 by 6
anonymous
  • anonymous
so, 126/210.
anonymous
  • anonymous
isn't it -7?
anonymous
  • anonymous
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.
anonymous
  • anonymous
Oh. Okay so then what does all of that mean? So 126/210 is k?
anonymous
  • anonymous
Yes. Simplify 126/210, though. (Divide num. and denom. by 2: 63/105)
anonymous
  • anonymous
Ugh. Okay, that's so complicated >.< Thanks!
anonymous
  • anonymous
haha. Yeah, a lot of math is complicated.
jim_thompson5910
  • jim_thompson5910
you need to reduce further 63/105 can be reduced further
anonymous
  • anonymous
by 3
jim_thompson5910
  • jim_thompson5910
divide both by 7 to reduce
anonymous
  • anonymous
right.
anonymous
  • anonymous
or 7. sorry.
anonymous
  • anonymous
Can you simplify it completely?
anonymous
  • anonymous
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
anonymous
  • anonymous
you cant have fractions in standard form. point slope form is fine with it.
anonymous
  • anonymous
What if I have to put it in standard form?
anonymous
  • anonymous
Then 2x+y=14 is in standard form.
anonymous
  • anonymous
And no fractions.
anonymous
  • anonymous
And x is positive. So it's fine.
anonymous
  • anonymous
Do you understand?
anonymous
  • anonymous
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(:
anonymous
  • anonymous
Yup. Any other questions?
anonymous
  • anonymous
Nope(: Gheez you're good
anonymous
  • anonymous
I'm gonna have another question on literal equations soon, so heads up xD
anonymous
  • anonymous
OK :)

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