Question

Direct Variation
Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x = 7.
1. y = 8 when x = -4

I'm not asking for the answer, I'd like if someone would explain how to do this because I don't understand it.

Answer 1

Direct variation means x times some constant is y. So, a direct variation would be of the form:
y = kx

They give us one point (x,y) = (-4,8).
So, y=8 when x=-4. Plug them in:
8 = k(-4)
k = -2

Ah, so we finally have our equation:
y = kx
y = (-2)x

And lastly, plug in x=7:
y = (-2)(7)
= -14

Answer 2

Thanks so much, thats the answer I got but could someone tell me if I got these two right also?
x=7
y=15 when x=6
My answer was "the equation y=2 relates x and y. When x=6, y=2(7), or 14

and

x=7
y=3 when x=9
I actually don't have an answer for this one because I got stuck at the dividing part:/

Answer 3

y = kx

substitute:
15 = 6k
k = 2.5

y = 7(2.5)

Answer 4

so when x = 7, y = 17.5

Answer 5

Oh ok thanks I fixed it. Could you help with the other one?

Answer 6

y = kx

3 = 9k
k = ?

Answer 7

I'm really confused because my textbook suggest that I divide 3 by 9 but that'd be 0.3. So should I just use 0.3 or flip it and divide 9 by 3?

Answer 8

3/9 = 1/3
so k = 1/3

Answer 9

Use 1/3 or 0.3?

Answer 10

use 1/3

Answer 11

y = 7(1/3)

Answer 12

2 1/3?

Answer 13

yea

Answer 14

Ok my final answer is "y = 1/3 relates x and y. 1/3(7), or 2 1/3."

Answer 15

I completely understand now thank you so much @AriPotta

Answer 16

shouldn't your final answer just be 2 1/3?

Answer 17

Yeah, but they want me to write a whole sentence

Answer 18

weird.

Answer 19

Yup