Given:
The equation that represents the relation between degrees Fahrenheit, F, and degrees Celsius, C.
[tex]F=\dfrac{9}{5}C+32[/tex]
To find:
Whether it is a proportional relationship or not.
Solution:
If y is proportional to x, then
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
where, k is constant of proportionality.
It means, the proportional relationship is in the form of [tex]y=kx[/tex] and (0,0) satisfy it.
We have,
[tex]F=\dfrac{9}{5}C+32[/tex]
Put C=0 and F=0.
[tex]0=\dfrac{9}{5}(0)+32[/tex]
[tex]0=0+32[/tex]
[tex]0=32[/tex]
This statement is not true because [tex]0\neq 32[/tex].
Since, (0,0) did not satisfy the equation [tex]F=\dfrac{9}{5}C+32[/tex], therefore, the given equation is not a proportional relationship.
