Answer:
Option C.
Step-by-step explanation:
A proportional relationship is defined as
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
where, k is the constant of proportionality.
From the given graph it is clear that there is proportional relationship with the point (-20,40).
Substitute x=-20 and y=40 in the above equation to find the value of k.
[tex]40=k(-20)[/tex]
Divide by -20.
[tex]-2=k[/tex]
The value of k is -2. So, the proportional relationship is defined as
[tex]y=-2x[/tex]
At x=-40,
[tex]y=-2(40)=-80[/tex]
It means point (-40,20) would not form a proportional relationship with the (-20,40).
Similarly,
At x=-10,
[tex]y=-2(-10)=20[/tex]
At x=15,
[tex]y=-2(15)=-30[/tex]
At x=5,
[tex]y=-2(5)=-10[/tex]
It means points (-10,-20) and (5,-15) would not form a proportional relationship with the (-20,40).
Only point (15,-30) would form a proportional relationship with the (-20,40).
Therefore, the correct option is C.
