Question

Does the equation 2x + 8= y represent a direct variation? If so, what is the constant of variation?

Answer 1

If it is direct variation, you should be able to multiply x by something to get y---no addition or subtraction.

y = 3x
y = .25x
y = (1/3)x

these are all direct variation

y = 3x + 2
y = .25x - 1
y = (1/3)x + 7

these are not direct variation

problems 1-3:
direct variation or not? solve each for y and see if there is any addition or subtraction over with the x. If there is, it is NOT direct variation. If you only have something multiplying the x (even an implied 1), the constant will be the coefficient of x.

problems 4-12:
figure out what you have to multiply x by to get y. In the end you need to get to:
y = ?x --where ? is whatever you'll multiply with x to get y.

or you could solve for ?---
y = ?x
y/x = ?x/x
y/x = ?

so to find out what ? is, simply divide y by x. Then write your equation in y = ?x format.

Hope that gives you enough help to do the work. It shouldn't be too bad.