Question

For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.A. yes; y=2xB. yes; y=3xC. yes; y=4xD. no; y does not vary directly with x.

Answer 1

We are given a table with values of "x" and associated values of "y". Let's remember that direct variation implies that each value of "y" will be related with its corresponding value of "x" according to the following relationship:

`y=kx`

Where "k" is the constant of proportionality. If the table shown has direct variation the same constant should apply for each value. Let's take the first value of the table, that is, x = 3 and y = 6. Substituting we get:

`6=k(3)`

Dividing both sides by 3 we get:

`(6)/(3)=k`

Solving the operations:

`2=k`

Now we substitute in the relationship:

`y=2x`

Now, for the second value of "x", that is x = 6:

`\begin{gathered} y=2(6) \\ y=12 \end{gathered}`

Since we did not get the corresponding value of "y" in the table, this means that the constant of proportionality doesn't work for this value, and therefore, "y" does not vary directly with "x".