Question

How do you determine whether y varies directly with x and if so, how do you find the constant of variation k for `- 5y = 5x + 10`?

Answer 1

`-5y = 5x +10`
could be simplified as
`y = -x -2`

According to
http://www.merriam-webster.com/dictionary/direct%20variation
Definition of DIRECT VARIATION
: mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other

from which it follows that the given equation is not a direct variation (i.e. `y` does not vary directly with `x`).

The equation of a line parallel to this which would be a direct variation would be
`y =-x`
or `y= (-1)x`
and for this equation the constant of variation would be `(-1)`