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

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Answer 1 · 2018-07-01T11:08:15

$No$ $color(blue)("No")$

Direct variation is expressed by:

$y \propto k x$ $y prop kx$

Where $k$ $bbk$ is the constant of variation.

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

Rearranging $883 x + y = 6$ $color(white)(88)3x+y=6$

$y = - 3 x + 6$ $y=-3x+6$

Comparing:

$y = - 3 x + 6$ $y=-3x+6$

$y = k x$ $y=kx$

As you can see these are not the same form, so $y = - 3 x + 6$ $y=-3x+6$ 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?