SOLUTION: Determine whether y varies directly with x. If so, find the constant of variation k and write the equation. x 6 18 54 162 y 24 72 216 648 Option

Question 7326: Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.
x
6
18
54
162
y
24
72
216
648
Options are: a. Yes k=4; y=4x b. yes, k = 3; y=3x c. yes, k=6; y= 6x d no
Ok, please tell me how to solve this problem and plus can u explain to me wht is direct variation? coz i believe this question's got sth to do with it.............thanks a lot!
Answer by longjonsilver(2297) (Show Source):
You can put this solution on YOUR website!
there are 2 simple variations...
1. x varies directly with y --> y x --> y = kx, where k is a constant
or
2. x varies indirectly with y --> y 1/x --> y = k/x, where k is a constant

in type 1, as x increases, so y increases.
in type 2, as x increases, so y decreases.

Looking at your numbers...as x increases, so y increases...looks pretty "direct" to me.

So, i am assuming that y=kx is the equation form that "explains" the numbers. We need to find k. So, put in some numbers...easy as that:

24 = 6k --> k=4

So, i believe all the pairs of numbers are generated by y=4x. You check it, to confirm this: put an x value in..do you get the y-values quoted in the question?

jon.