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Q: How do you know if the equation is a direct variation?

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There are three ways: a table, a graph, and an equation.

find the direct variation equation 3x+y=0

There is only one equation that is given in the question and that equation is not a direct variation.

No. This is not true. It is false. The equation is an example of direct variation.

equation, table or a graph

Without the rest of the equation it is not possible to tell. * * * * * If the equation is in the form y = k*x where k is a non-zero constant, then it is.

Graphs of direct variation pass through the origin so the y-intercept would be 0.

For a direct variation equation the constant MUST be 0. Then the ratio of a pair of values of the two variables is the slope.

y=3x is a direct variation in that y varies directly with x by a factor of 3. Any linear equation (a polynomial of degree 1, which is a polynomial equation with a highest exponent of 1), is a direct variation of y to x by some constant, and this constant is simply the coefficient of the "x" term. Other examples: y=(1/2)x is a direct variation, and the constant of variation is 1/2 y=-9x is a direct variation, and the constant of variation is -9

Without an equality sign the information given does not represent an equation.

Without an equality sign the given expression can't be considered to be an equation.

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.

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