Does the following equation represent a direct variation? If so, what is the constant of variation, k?
2y = -6x
A. Yes, k = -3 ~~~
B. Yes, k = -6
C. Yes, k = -⅓
D. It is not a direct variation
My answer is A. Am I right?
you are correct
Thank you!
Yes, your answer is correct. The equation 2y = -6x represents a direct variation, and the constant of variation, k, can be found by rearranging the equation to the form y = kx. In this case, dividing both sides of the equation by 2 gives y = -3x, so the constant of variation, k, is -3. Therefore, the correct answer is A.
Yes, you are right. The given equation, 2y = -6x, represents a direct variation. In a direct variation, the variables are directly proportional to each other, which means that as one variable increases, the other also increases or decreases by a constant factor.
To determine the constant of variation, k, we need to isolate y in terms of x. Divide both sides of the equation by 2:
2y/2 = -6x/2
This simplifies to:
y = -3x
Comparing it to the general form of a direct variation equation, y = kx, we can see that the constant of variation, k, is -3. Therefore, the correct answer is A. Yes, k = -3.