What is the direct variation equation if y varies directly with x and
y = –5 when x = –15?
a. y= -10x
b. y= -3x
c. y= 3x
d. y= x

The answer is D. Even without plugging the answer choices in (which is an option), you know that 5 is 1/3 of 15 and 15 is 3 times 5. So if you multiply -15 by 1/3, you get -5. 

Direct variation is written in the form y = kx, where k is the constant of proportioanlity. To find k, substitute the given values y = -5 and x = -15 into the direct variation equation y = kx and solve for k.

y = kx
(-5) = k(-15)
k = 1/3

Now we rewrite the equation using the value of k.
y = (1/3)x