Given:
The graphed point is (60,-20).
To find:
The ordered pair that would form a proportional relationship with the given point.
Solution:
If y is proportional to x, then
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
[tex]\dfrac{y}{x}=k[/tex]
Where, k is the constant of proportionality.
For the given point,
[tex]k=\dfrac{-20}{60}[/tex]
[tex]k=\dfrac{-1}{3}[/tex]
For option (A),
[tex]k=\dfrac{30}{-10}[/tex]
[tex]k=-3\neq \dfrac{-1}{3}[/tex]
For option (B),
[tex]k=\dfrac{-15}{30}[/tex]
[tex]k=-\dfrac{1}{2}\neq \dfrac{-1}{3}[/tex]
For option (C),
[tex]k=\dfrac{10}{-30}[/tex]
[tex]k=\dfrac{-1}{3}[/tex].
The point (-30,10) gives the same value of the constant of proportionality. So, the point (-30,10) forms a proportional relationship with the given point.
Therefore, the correct option is C.
