For this case we have that by definition, if the variables "y" and "x" have a proportional relation, and[tex]y = 9[/tex]when [tex]x = 2[/tex], then:
[tex]\frac {x} {y} = \frac {2} {9}[/tex]
Now, we want to know the value of the variable "y" when [tex]x = 3[/tex], then:
[tex]\frac {3} {y} = \frac {2} {9}[/tex]
Clearing "y" we have:
We multiply by "y" on both sides of the equation:
[tex]y * \frac {3} {y} = y * \frac {2} {9}\\3 = \frac {2y} {9}[/tex]
We multiply by 9 on both sides:
[tex]9 * 3 = \frac {2y} {9} * 9\\27 = 2y[/tex]
We divide by 2 on both sides:
[tex]\frac {27} {2} = \frac {2y} {2}\\y = 13.5[/tex]
So, when [tex]x = 3[/tex]then[tex]y = 13.5[/tex]
Answer:
[tex]y = 13.5[/tex]
