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Q: Is direct variation a special case?

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A direct variation (!) or direct reelationship.

Yes, it is direct variation.

No, it is not a direct variation.

I have recently been doing all these direct variation problems but not every linear relationship is a direct variation... But every direct variation is a linear relation!

If a variable X is in inverse variation with a variable Y, then it is in direct variation with the variable (1/Y).

Direct variation is the ratio of two variable is constant. Inverse variation is when the product of two variable is constant. For example, direct variation is y = kx and indirect variation would be y = k/x .

Yes. y = 1x is the same as y = x which is the simplest case of direct variation. If you consider the equation y = mx + b, then a direct variation will always have b = 0 (i.e. the graph goes through the origin). The value of m is called the "constant of variation", and the equation is usually written as y = kx.

When two variables are related in such a way that the ratio of their values always remains the same, the two variables are said to be in direct variation. y=2x is direct variation y=x+2 is not direct variation

The slope of the graph of a direct variation is always positive.

No. The origin must be a solution for any direct variation.

find the direct variation equation 3x+y=0

Yes, you can have a negative coefficient in a direct variation. So if you had y = -7x, that would be a direct variation. If you have y = -x, I do not know, if that is what you mean. Hope it helped.

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