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= (1)/(3)x

Question

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=
`(1)/(3)`x

Answer 1

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

Answer 2

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.