algebra 2 help?

Question

The resistance (R) of a copper wire varies directly as its length (L). Write this relation as a formula using k as the constant of variation.

A k/L=R
B K/R=L
C LRk=0
D R/L=k
E RL=k
F Rk=L

Answer 1

To be directly proportional means that the one multiplied by some constant equals the other.

The equation that matches that definition is:

F - R * k = L

So if R is twice as much, L must also be twice as much to satisfy the condition.

Actually also this satisfies the condition:

D - R / L = k

Because if R is twice as high, also L must be twice as long for the result to be a constant value.

Also both equations are equivalent ... only that the k in D is 1/k from F.

Answer 2

HAHA you got 3 different answers, if the two numbers varies directly, this means they are directly proportional so as one increases the other must increase also, so basically R=L throw in a constant to some side and you get F, or D

its not E because you will have R=k/L that's inversely proportional, as L gets big R gets small

it can be D because you move L over to the right and you get R=Lk, if R gets bigger L does also, the same with F

A and B are the same thing as E, they are inversely proportionally,

Answer 3

Varies directly implies they are related in such a way that if one gets higher then the other one gets higher, and vice versa. First thing you should find is a relationship that shows direct variation, which in this case is E and F, but you can see that E and F are different.

Further assessment of the problem, indicates that there is a constant of variation. It means that the constant of variation is the one that you will use to multiply one of the variables(either R or L).

For many cases, direct variability means multiplication(in some context) but don't forget that multiplication is just the reverse of division.

Now it is hard to decide which because I am presented with 3 possible choices, namely D,E, & F.

D manipulated becomes F and vice versa
E shows direct proportionality to each other so the choice lies
with you on what your context of "constant of variation" means, whether you will use it to divide or to multiply.:)

Answer 4

D and F will both work.

Answer 5

f

Answer 6

e