Question

Does the given equation represent direct variation? If so, what's the constant of variation?

a) Yes, constant of variation is 10/6.
b) Yes, constant of variation is 16/(xy).
c) No, it does not represent direct variation.
d) Yes, constant of variation is 10x² - 6y².

Answer 1

The given equation does not represent direct variation.

Step-by-step explanation:

The given equation represents direct variation if it can be written in the form y = kx, where k is the constant of variation. Let's analyze each option:

1. a) Yes, constant of variation is 10/6. This option does not represent direct variation because the constant of variation should be a single value, not a fraction.
2. b) Yes, constant of variation is 16/(xy). This option does not represent direct variation because the constant of variation should be a constant value, not a variable expression.
3. c) No, it does not represent direct variation. This option is correct because it states that the equation does not represent direct variation.
4. d) Yes, constant of variation is 10x² - 6y². This option does not represent direct variation because the constant of variation should be a constant value, not a variable expression.

Therefore, the correct answer is c) No, it does not represent direct variation.