Question

How do you determine whether an equation represents a direct variation and if so its constant variation?

Examples:

1. 7x=-6y
2.7x+2y=0

I did divide them, but I keep on getting decimals and I'm lost on how the answer choices aren't the same as what I got.

Answer 1

If you divide y by x and get a constant, it is a direct variation and the constant is the quotient of y/x

Answer 2

a direct variation can be put in the form y = k*x where k is a constant (called the constant of variation, imaginatively enough).

an indirect variation can be put in the form y = k/x where k is a constant, I bet you can guess the name :-)

if you have something like your examples, you've got direct variation. if however you have a +3 or -7 or some other expression in there, such as 7x = -6y + 2, you no longer have a direct variation, but rather a linear relationship.