Is 5x - 3y equals 0 a direct variation?
yes.
3y = 5x
y = (5/3)x
To determine if the equation 5x - 3y = 0 represents a direct variation, we need to check if it can be written in the form y = kx, where k is a constant.
Rearranging the given equation, we have:
5x - 3y = 0
Adding 3y to both sides:
5x = 3y
Dividing both sides by 3:
(5/3)x = y
The equation can be written as y = (5/3)x, which is in the form y = kx. Therefore, the equation 5x - 3y = 0 represents a direct variation.
To determine if the equation 5x - 3y = 0 represents a direct variation, we can analyze its form. A direct variation is a linear equation in the form y = kx, where k is the constant of variation.
To check if the given equation can be written in the form y = kx, we need to isolate y. Rearranging the equation, we get:
5x - 3y = 0
-3y = -5x
y = (5/3)x
Comparing this equation with the form y = kx, we can see that the coefficient of x is (5/3), which is a constant value. Therefore, we can conclude that the equation 5x - 3y = 0 represents a direct variation, since it can be written as y = (5/3)x.
In summary, yes, 5x - 3y = 0 is a direct variation because it can be rewritten as y = (5/3)x.