Answer:
, ![(9,6)](https://tex.z-dn.net/?f=%289%2C6%29)
Step-by-step explanation:
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 and the line passes through the origin
Verify each case
case A) For
point ![(9,6)](https://tex.z-dn.net/?f=%289%2C6%29)
The linear direct variation equation is equal to
![y=(2/3)x](https://tex.z-dn.net/?f=y%3D%282%2F3%29x)
For ![x=9, y=6](https://tex.z-dn.net/?f=x%3D9%2C%20y%3D6)
substitute the value of x and the value of y in the equation and then compare the result
![6=(2/3)(9)](https://tex.z-dn.net/?f=6%3D%282%2F3%29%289%29)
------> is true
therefore
This line represent a direct variation
case B) For
point ![(6,9)](https://tex.z-dn.net/?f=%286%2C9%29)
The linear direct variation equation is equal to
![y=(2/3)x](https://tex.z-dn.net/?f=y%3D%282%2F3%29x)
For ![x=6, y=9](https://tex.z-dn.net/?f=x%3D6%2C%20y%3D9)
substitute the value of x and the value of y in the equation and then compare the result
![9=(2/3)(6)](https://tex.z-dn.net/?f=9%3D%282%2F3%29%286%29)
------> is not true
therefore
This line not represent a direct variation
case C) For
point ![(9,-6)](https://tex.z-dn.net/?f=%289%2C-6%29)
The linear direct variation equation is equal to
![y=(2/3)x](https://tex.z-dn.net/?f=y%3D%282%2F3%29x)
For ![x=9, y=-6](https://tex.z-dn.net/?f=x%3D9%2C%20y%3D-6)
substitute the value of x and the value of y in the equation and then compare the result
![-6=(2/3)(9)](https://tex.z-dn.net/?f=-6%3D%282%2F3%29%289%29)
------> is not true
therefore
This line not represent a direct variation
case D) For
point ![(9,6)](https://tex.z-dn.net/?f=%289%2C6%29)
The linear direct variation equation is equal to
![y=-(2/3)x](https://tex.z-dn.net/?f=y%3D-%282%2F3%29x)
For ![x=9, y=6](https://tex.z-dn.net/?f=x%3D9%2C%20y%3D6)
substitute the value of x and the value of y in the equation and then compare the result
![6=-(2/3)(9)](https://tex.z-dn.net/?f=6%3D-%282%2F3%29%289%29)
------> is not true
therefore
This line not represent a direct variation