Does the equation $3x + y = 6$ represent a direct variation and if so, identify the constant of variation?

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Answer 1 · 2018-07-01T11:08:15

$color(blue)("No")$

Direct variation is expressed by:

$y prop kx$

Where $bbk$ is the constant of variation.

$prop$ is used to represent proportion, but you will often see this replaced by the equality symbol $=$

Rearranging $color(white)(88)3x+y=6$

$y=-3x+6$

Comparing:

$y=-3x+6$

$y=kx$

As you can see these are not the same form, so $y=-3x+6$ doesn't represent direct proportion/variation.

Does the equation 3x + y = 63x + y = 6 represent a direct variation and if so, identify the constant of variation?