A proportional relationship is also a direct variation.
The general equation of direct cvariation is
y = kx,
where k is a number.
In your case, if k = -1, then y = kx becomes y = (-1)x which is the same as
y = -x
6(2k-3) is the answer to this problem.
make a distributive
take the 6 out of the equation and u have remaining 2k-3. 6(2k-3)
If there are 45 beads, with a ratio of
![1:4](https://tex.z-dn.net/?f=1%3A4)
Then,
![\frac{45}{5}=9](https://tex.z-dn.net/?f=%5Cfrac%7B45%7D%7B5%7D%3D9)
Then if
![\frac{1}{4}=\frac{9}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%3D%5Cfrac%7B9%7D%7Bx%7D)
Then
![x=9*4](https://tex.z-dn.net/?f=x%3D9%2A4)
Therefore,
![x=36](https://tex.z-dn.net/?f=x%3D36)
Meaning, there would be a ratio of 36 beads to 9 beads
-- Find how much 'y' changes from the first point to the second one.
-- Find how much 'x' changes from the first point to the second one.
-- The slope of the line going from the first point to the second one is
(change in 'y') / (change in 'x') .
The rise of -7 means that there is 7 less. The fall of 7 would mean that it is also 7 less. So, yes. They are both the same thing.