Question

For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation. x|y 4|28 6| 48| 8| 72
A. yes; y = 2x
B. yes; y = 5x
C. yes; y = 7x
D. no; y does not vary directly with x

Answer 1

Let's have a look:

2(4)= 8 (this would not work)

5(4)= 20 (this wouldn't work)

7(4)= 28 This does, let's check the others.

7(6)= 42 This does not work.

"D" would be the correct answer.

I hope this helps!
~cupcake

Answer 2

Answer:

The answers is D.

Step-by-step explanation:

That $y$ varies directly with $x$ means that there exist a constant $k$ such that $y = kx$. If we suppose that $y$ varies directly with $x$ , then

$4k = 28$ , $6k = 48$ and $8k = 72$,

from where we get

$k = \frac{28}{4}$, $k = \frac{48}{6}$ and $k = \frac{72}{8}$

and hence

$k = 7$, $k = 8$ and $k = 9$.

Since the value of $k$ is not constant, then $y$ does not vary directly with $x$.