Question

Does the following table represent direct variation? If yes, write theequation

Answer 1

A direct variation means that when one variable increase the other variable increases too, and when a variable decrease, the other variable decrease too. The increase and decrease follow a factor of variability, or slope.

To find the equation of a situation as given you need to find the slope and the y-intercept (the value of the function when the independient variable is 0)

Slope: You can use the next formula to find the slope in this situation:

`m=\frac{y_2-_{}y_1}{x_2-x_1}`

In the given table the first column is the independient variable (x) and the second column is the dependient variable (y).

`m=(20-12)/(5-3)=(8)/(2)=4`

The slope of the given variation is m=4

Y-intercept: You use one row of data to find the y-intercept: (b)

`\begin{gathered} y=mx+b \\ 12=4(3)+b \\ 12=12+b \\ 12-12=b \\ 0=b \end{gathered}`

As the slope is m=4 and the y-intercept is b=0 you get the next equation:

`y=4x`Then, the correct answer is yes, y = 4x