Determine whether y varies directly with x. If so, find the constant of variation and write the function rule.
x y
-2 3
1 4
2 7

Question

Determine whether y varies directly with x. If so, find the constant of variation and write the function rule.
 x    y
-2   3
 1    4
 2    7

anonymous · Answer

$$y=kx$$ is the format for direct variation. This means that y varies with x. It can also be read is y is proportional to x. What it wants us to do is first determine the proportional factor k and use that to see if x always varies with y.

We can start by taking the first values of x and y
$$3=-2k$$
By solving for k, we get -3/2.

Plug in the next sets of values for x and y and our newly found k and see if you get a true statement. If you do (ex: 5=5 or 2=2. . .) then that means x and y are directly proportional.

Another way you could do it is plug in the first set of x and y values and solve for k, and then plug in the second set of x and y values and solve for k, then the third set, etc. If any of the k's are different, then y does not vary with x since it requires different proportional factors.