Direct variable and porportion

T

TheKeyboardist

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Aug 30, 2005
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My teacher taught this as a lesson in class today but i dont really understand this. For hw, he gave out proplems saying "y equals directly as x. Find the constant of variation, and write a equation of direct variation that relates the two variables"

An example of a question is

y=-6/7 whne x=-18/35

Just an explanation how to do this kind of problem would help alot. Thanks!
 
I think you mean "y varies directly as x"...?

Variation equations translate as follows:

. . . . ."y varies directly as x": y = kx

. . . . ."y varies inversely as x": y = k/x

. . . . ."y varies jointly with x and z": y = kxz

Plug in whatever values they give you, and solve for the value of k. Then plug k into the equation, and evaluate at whatever x they want you to find y for.

Eliz.
 
oh, yea! Thats what i meant. I dunno what i was thingking of when i typed that =P

I dont understand what you mean when you said:

"Then plug k into the equation, and evaluate at whatever x they want you to find y for. "

On my first rough try, i got k as -5/3 in my example. So what do i do with it? just write down y=-5/3x as my answer?

Thanks for your help stapel.
 
How did you get a negative value for k? The product of two negative numbers is positive, but y is given as being negative. So k cannot be negative, or kx, with x negative, wouldn't be negative y = -6/7.

. . . . .y = kx

. . . . .For x = -18/35, we have y = -6/7.

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

. . . . .[-6/7][-35/18] = k

. . . . .[6/7][35/18] = k

. . . . .[1/7][35/3] = k

. . . . .[1/1][5/3] = k

. . . . .5/3 = k

Then y = (5/3)x.

Eliz.
 
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