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Is the problem y equals 3x a direct variation if so what is the constant of variation?
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
Can a system of two direct variation equations have no solutions?
No. The origin must be a solution for any direct variation.
Can ax plus by equals c be a direct variation if a and b and c does not equal 0?
No, direct variation is "y=ax." In direct variation a equals any real constant, b=1, and c must equal zero. If any of thee conditions are changed, it is not direct variation.
Which of the following represents a direct variation function?
Any function of the form Y = cX where X and Y are variables and c is a constant.
What of an equation is any value that makes the equation true?
Such an equation is called an IDENTITY.
