Question

Suppose y varies directly with x, and y = 14 when x = -4. What is the value of y when x = -6? Can anyone help me with this? Like explain it because I don't understand it like how does this work?

Answer 1

y varies directly with x

means
y = k*x
where k is some number

your first step is find k

start with y = 14 when x = -4
replace y with 14 and x with -4 in the y=k*x equation:
14= k* -4

can you "solve for k"? (divide both sides by -4)

Answer 2

14/-4 = k*-4/-4
-3.5 = k?
right?

Answer 3

Wait but the choices on it says
a. -21
b. 10
c. 18
d. 21

Answer 4

so far, so good. k= -3.5

now you know k, so "direct variation" means
y = -3.5 x

to find y, replace x with a number.
What is the value of y when x = -6?

Answer 5

The idea is multiply x times -3.5. If x is -6, that means multiply -6*-3.5
to get the y

Answer 6

okay so it would be 21?

Answer 7

so d?

Answer 8

yes.

To summarize

direct variation means
y = k x

find k (you need an x and a y value to do that)
once you know k, you can find y for any other x they give you.

Answer 9

Thanks you helped me a lot! :)