Answer:
Part 1) ![y=3](https://tex.z-dn.net/?f=y%3D3)
Part 2) ![x=\frac{1}{3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%7D%7B3%7D)
Step-by-step explanation:
<u><em>The correct question is</em></u>
1) Suppose y varies directly as x, and y equals nine when x equals three seconds. Find y when x equals one
2) Suppose y varies directly as x, and y equals nine when x equals three seconds. Find x when y equals one
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
or ![y=kx](https://tex.z-dn.net/?f=y%3Dkx)
Part 1) we have that
For x=3, y=9
Find the value of k
substitute the value of x and y
----> ![k=\frac{9}{3}=3](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B9%7D%7B3%7D%3D3)
the linear equation is
![y=3x](https://tex.z-dn.net/?f=y%3D3x)
so
For x=1
substitute in the linear equation and solve for y
![y=3(1)=3](https://tex.z-dn.net/?f=y%3D3%281%29%3D3)
Part 2) we have that
For x=3, y=9
Find the value of k
substitute the value of x and y
----> ![k=\frac{9}{3}=3](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B9%7D%7B3%7D%3D3)
the linear equation is
![y=3x](https://tex.z-dn.net/?f=y%3D3x)
so
For y=1
substitute in the linear equation and solve for x
![1=3x](https://tex.z-dn.net/?f=1%3D3x)
Divide by 3 both sides
![x=\frac{1}{3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%7D%7B3%7D)