Question

How do you tell wether the equation `3x + y = 6` represents direct variation and if so, how do you identify the constant of variation?

Answer 1

The equation does not represent direct variation. Consequently, there is no constant of variation.

Explanation:

You can determine whether or not an equation represents direct variation by first rewriting it in slope-intercept form:

`y=mx+b`

where:
`y=`y-coordinate
`m=`slope
`x=`x-coordinate
`b=`y-intercept

In direct variation, `b`, the y-intercept, is `0`. However, if you rearrange your equation into slope-intercept form, you will find that the y-intercept is not `0`:

`3x+y=6`

`y=-3x` `color(red)(+6)`

In this case, the y-intercept is `6`. Since it is not `0`, this equation does not represent direct variation. Consequently, there is no constant variation since the equation does not follow the general equation, `y=mx+0`.