How do you tell wether the equation 3x + y = 63x+y=6 represents direct variation and if so, how do you identify the constant of variation?

1 Answer
Johnson Z.
Feb 1, 2016

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+by=mx+b

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

In direct variation, bb, the y-intercept, is 00. However, if you rearrange your equation into slope-intercept form, you will find that the y-intercept is not 00:

3x+y=63x+y=6

y=-3xy=−3x color(red)(+6)+6

In this case, the y-intercept is 66. Since it is not 00, this equation does not represent direct variation. Consequently, there is no constant variation since the equation does not follow the general equation, y=mx+0y=mx+0.

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