Respuesta :
Given:
[tex]F=\dfrac{9}{5}C+32[/tex]
where, F is degree Fahrenheit and C is degree Celsius.
To find:
Whether there is a proportional relationship between C and F.
Solution:
We know that, proportional relations is defined as
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
where, k is constant of proportionality.
So, the line of proportional relationship passes through (0,0) and the equation must be true for (0,0).
If there is a proportional relationship between C and F, then the equation must be true for (0,0).
Substituting F=0 and C=0 in the given equation, we get
[tex]0=\dfrac{9}{5}(0)+32[/tex]
[tex]0=0+32[/tex]
[tex]0=32[/tex]
This statement is false because [tex]0\neq 32[/tex].
It means the line of given equation does not passes through (0,0). So, it s not a proportional relationship.
Hence, there is not a proportional relationship between C and F.
