Answer:
Option B). (6,8),(0,0),(18,24)
Step-by-step explanation:
<u><em>The options of the question are</em></u>
A). (2,4),(0,2),(3,9)
B). (6,8),(0,0),(18,24)
C). (3,6),(4,8),(9,4)
D). (1,1),(2,1),(3,3)
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
or
In a proportional relationship the constant of proportionality k is equal to the slope m of the line <u><em>and the line passes through the origin</em></u>
Verify each case
case A) (2,4),(0,2),(3,9)
This set of points not represent a proportional relationship because in a proportional relationship the intercepts must be equal to (0,0) and this set of points have the point (0,2)
case B) (6,8),(0,0),(18,24)
Find the constant of proportionality k
![k=\frac{y}{x}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7By%7D%7Bx%7D)
For x=6, y=8 ----> ![k=\frac{8}{6}=\frac{4}{3}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B8%7D%7B6%7D%3D%5Cfrac%7B4%7D%7B3%7D)
For x=18, y=24 ----> ![k=\frac{24}{18}=\frac{4}{3}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B24%7D%7B18%7D%3D%5Cfrac%7B4%7D%7B3%7D)
The line passes through the origin
The linear equation is
![y=\frac{4}{3}x](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B4%7D%7B3%7Dx)
so
This set of points could be n the line that Sara graphs
case C) (3,6),(4,8),(9,4)
Find the constant of proportionality k
![k=\frac{y}{x}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7By%7D%7Bx%7D)
For x=3, y=6 ----> ![k=\frac{6}{3}=2](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B6%7D%7B3%7D%3D2)
For x=4, y=8 ----> ![k=\frac{8}{4}=2](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B8%7D%7B4%7D%3D2)
For x=9, y=4 ----> ![k=\frac{4}{9}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B4%7D%7B9%7D)
The values of k are different
therefore
This set of points not represent a proportional relationship
case D) (1,1),(2,1),(3,3)
Find the constant of proportionality k
![k=\frac{y}{x}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7By%7D%7Bx%7D)
For x=1, y=1 ----> ![k=\frac{1}{1}=1](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B1%7D%7B1%7D%3D1)
For x=2, y=1 ----> ![k=\frac{1}{2}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B1%7D%7B2%7D)
The values of k are different
therefore
This set of points not represent a proportional relationship