Help: Find the constant of variatin for a direct variation that includes the given values.?

Question

Help: Find the constant of variation for a direct variation that includes the given values.
(2,4)

Note: This is not my homework, im studying for the semester exams and stumble across this material which im having difficulty on. Plz help by showing the work.

Answer 1

Since it is a direct variation we can use the formula

y = k x

Since we are given the ordered pair (2,4) we know y=4 when x=2. Plugging these values into the formula gives us

4 = k(2)

To solve for k we divide both sides by 2 which gives us

k = 2.

It would also be correct to set up the variation to be

x = k y

In this case, we do the same procedures to find k. Plug in the known values for x and y to get that k = 1/2. Unless you are told which one to solve for either are correct. If you are given a multiple choice test I would think that only one could be a possible answer, unless you are first given the variation equation.

Answer 2

You need to give more information than this. It can't be done with just two numbers. You need at least an equation showing the relationship between the numbers as one variable changes. For example, with the two numbers given here, if we let 2 = x and 4 = y, then we could write it in this form:

y = cx, where c is the constant of variation.

Then, plugging in 4 for y and 2 for x, we get 4 = c(2). Dividing through by 2 gets us c = 2.

But the relationship could just as well be y = cx^2, in which case, after plugging in x and y, c would be equal to 1.

Answer 3

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