Given:
[tex]y=\dfrac{3}{4}x[/tex]
[tex]y=\dfrac{1}{2}x-6[/tex]
To find:
Whether the above functions are proportional or non-proportional?
Solution:
If y is proportional to x, then
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
where, k is constant of proportionality.
The proportional relationships are in the form of [tex]y=kx[/tex] and they passes through (0,0).
Putting x=0 and y=0 in the given equations.
[tex]y=\dfrac{3}{4}x[/tex]
[tex]0=\dfrac{3}{4}(0)[/tex]
[tex]0=0[/tex]
It is a true statement.
[tex]y=\dfrac{1}{2}x-6[/tex]
[tex]0=\dfrac{1}{2}(0)-6[/tex]
[tex]0=0-6[/tex]
[tex]0=-6[/tex]
It is a false statement.
Therefore, [tex]y=\dfrac{3}{4}x[/tex] is proportional and [tex]y=\dfrac{1}{2}x-6[/tex] is non-proportional.
