Asked by TyTy

This is kind of like the first question I asked, and I'm still having a little trouble on it.

The Ordered pairs in each exercise are for the same direct variation.
Find the missing value.

(-2,8) and (x,12)

I'm not sure how to work out the problem.
Answered by TyTy
I'm not sure but if i cross multiply the two coordinates, i think the answer is...

x=-3?
Answered by Writeacher
Cross-multiplying seems to be the process:
http://www.jiskha.com/display.cgi?id=1199568727

So ...

-2/8 = x/12
8x = -24
x = -3

Right?
Answered by TyTy
yes, x=-3
Answered by Damon
Although I am sure I will be called on the carpet for saying why, I will try anyway.
If it is a direct variation it is a straight line of form:

y = k x
put in your first point
8 = -2 x
so k = -4
NOW any other point on this line satisfies
y = -4 x
so put in 12 for y
12 = -4 x
x = -3 as you know from "cross multiplying"
Answered by TyTy
yes, that's the way I didn't understand how to do before.
Answered by Damon
By the way, these problems are a special case of direct variation, linear.
The relation could be quadratic, cubic quartic ....
but is always of form y = k x^n
Here so far we are assuming that n = 1
Answered by Damon
Do you get it now?
Answered by Damon
Fixing typo and expanding

y = k x
put in your first point
8 = -2 k
solve that for k
so k = -4
NOW any other point on this line satisfies
y = -4 x
so put in 12 for y
12 = -4 x
x = -3 as you know from "cross multiplying"
Answered by TyTy
Um, i did until you mention the linear part.
Answered by Damon
I do not think you will get direct variation that is quadratic etc in this course or they would have mentioned it. For now assume direct variation means y = k x
Answered by TyTy
Ok , thank you for your help.
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