how do you find the constant of variation k for the direct variation?
for example, 4x + -6y. how do you find k?
If you had
6 y = 4 x
y = (4/6) x
y = (2/3) x
If you had
6 y = -4 x
y = (-2/3) x
Of course direct variation is not always linear.
If 6 y = 4 x^3
then y = (2/3) x^3
To find the constant of variation (k) in a direct variation equation, such as 4x + -6y = 0, you need to isolate the variable y and then express it in terms of x. The equation can be rearranged as follows:
4x + -6y = 0
First, move the term containing x to the other side of the equation:
-6y = -4x
Next, divide both sides of the equation by -6 to isolate y:
y = (4/6)x
Now, you can simplify the fraction:
y = (2/3)x
Comparing this equation to the general form of a direct variation equation, which is y = kx, you can see that the constant of variation (k) in this case is 2/3.
To find the constant of variation, k, in a direct variation equation, such as 4x + -6y, you need to compare the coefficients of the variables.
In this equation, the coefficient of x is 4, and the coefficient of y is -6.
The constant of variation, k, is the ratio between these coefficients. To calculate k, you divide the coefficient of y by the coefficient of x:
k = coefficient of y / coefficient of x
In this case, k = -6 / 4 = -3/2.
Therefore, the constant of variation, k, for the direct variation equation 4x + -6y is -3/2.