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August 16th, 2013, 10:30 AM   #1
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Direct and Inverse Variation

Question: {{Studying for the SAT}}
The quantities x and y are directly proportional if y=kx for some constant k. For example: x and y are directly proportional. When the value x is 10, y is equal to -5. If x=3, what is y?
Because x and y are directly proportional, y=kx for some constant k. You know y is -5 when x is 10; you can use this to find k.

y=kx
-5=k(10)
k= -1/2
<---- this is what i am confused about how am i supposed to know the 10/-5 is supposed to equal -1/2 instead of -2?? I understand
that obviously is half of 10 but.... ?

Goes on to say:
So, the equation is y=-1/2x. When x=3, you get y=(-1/2)(3)= -3/2

Is it supposed to be a fraction for Direct and Inverse Variations? This is what confuses me in math, how i am supposed to know what kind of equation it is and what formula to use...
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August 16th, 2013, 10:49 AM   #2
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Re: Direct and Inverse Variation

Quote:
Originally Posted by chelsf123
Question: {{Studying for the SAT}}
The quantities x and y are directly proportional if y=kx for some constant k. For example: x and y are directly proportional. When the value x is 10, y is equal to -5. If x=3, what is y?
Because x and y are directly proportional, y=kx for some constant k. You know y is -5 when x is 10; you can use this to find k.

y=kx
-5=k(10)
is absolutely correct. Tell me what you did to both sides of this equation to find ?
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August 16th, 2013, 07:40 PM   #3
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Re: Direct and Inverse Variation

divided both sides by -5 so it would come out to be -2 or -1/2 right so what i didnt understand is why they wrote it as -1/2 instead of -2 do you get what im saying? do you have to use fraction form for the constant?
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August 16th, 2013, 07:41 PM   #4
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Re: Direct and Inverse Variation

or would you divide both sides by 10?
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August 17th, 2013, 07:53 AM   #5
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Re: Direct and Inverse Variation

The quantities x and y are directly proportional if y=kx for some constant k. For example: x and y are directly proportional. When the value x is 10, y is equal to -5. If x=3, what is y?
Because x and y are directly proportional, y=kx for some constant k. You know y is -5 when x is 10; you can use this to find k.

Directly proportional so we use the equation y=kx.

-5=k10 --->divide both sides by 10---> k=-1/2

To find y when x=3:

y=kx
y=(-1/2) * (3)
y= -3/2

Hope this helps.
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August 17th, 2013, 07:56 AM   #6
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Re: Direct and Inverse Variation

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Originally Posted by chelsf123
or would you divide both sides by 10?
You are solving for k. So, you want to get k by itself. If you divide by -5, you won't completely have the K value itself. You want to know the "k" value so you can plug it back into the y=kx equation when you know the given value of x (which equals to 3) so you can solve for y.
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