It is -4.
The equation ( y = 4x + 1 ) is not a direct variation. In a direct variation, the relationship can be expressed in the form ( y = kx ), where ( k ) is a constant and there is no constant term added or subtracted. Since this equation includes the constant term ( +1 ), it does not meet the criteria for direct variation.
To determine if ( y = kx ) represents a direct variation, ( y ) must vary directly as ( x ) with a constant ratio ( k ). The expression ( y = 4x ) indicates that ( y ) is directly proportional to ( x ) with a constant of variation ( k = 4 ). Thus, yes, ( y = 4x ) is indeed a direct variation.
6y = 4x^2 y = (4/6)x^2 y = (2/3)x^2 Option B: 2/3
1
No, it is not a direct variation.
The equation ( y = 4x + 1 ) is not a direct variation. In a direct variation, the relationship can be expressed in the form ( y = kx ), where ( k ) is a constant and there is no constant term added or subtracted. Since this equation includes the constant term ( +1 ), it does not meet the criteria for direct variation.
6y = 4x^2 y = (4/6)x^2 y = (2/3)x^2 Option B: 2/3
4x= y
1
1
No, it is not a direct variation.
50
find the constant of variation and the slope of the given line from the graph of y=2.5x
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
y equals 4x+1 is a parallel line to y equals 4x.
y = kx: 10 = 37k so k = 10/37 and y = 10x/37
In the equation ( y = 4X ), the constant of proportionality is 4. This means that for every unit increase in ( X ), ( y ) increases by 4 units, indicating a direct proportional relationship between ( y ) and ( X ). Thus, ( y ) is directly proportional to ( X ) with a proportionality constant of 4.