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
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.
Tell whether the equation -4x+ 2y = -2 represents a direct variation. If so, identify the constant of variation.
No, it is a linear equation which does not pass through the origin unless B = 0. If B = 0 then Y and X could be said to vary in direct proportion and M would be the constant of variation, not the whole equation.
variation
an equation of the form y = kx k is the constant of variation
The equation is xy = k where k is the constant of variation. It can also be expressed y = k over x where k is the constant of variation.
The equation is xy = 22.5
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
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.
Tell whether the equation -4x+ 2y = -2 represents a direct variation. If so, identify the constant of variation.
No, it is a linear equation which does not pass through the origin unless B = 0. If B = 0 then Y and X could be said to vary in direct proportion and M would be the constant of variation, not the whole equation.
variation
y = kx, where k is a constant, and x and y are the two variables.
xY = 6.
y = k/x of xy = k where k is a constant.
Two variables, X and Y are said to be in inverse variation if XY = k or Y = k/X for some constant k.