The answer and explanation is in the image.
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we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y/x=k or y=kx
so
That means it's the equation of a line passing through the origin.
case a) and case d) are discarded because the line does not pass through the origin
<u>case b) we have</u>
for x=2 y=4
y/x=k-------> 4/2=2------> k=2
y=2x-------> in this case the value of y is two times the value of x
<u>case c) we have</u>
for x=4 y=2
y/x=k-------> 2/4=1/2------> k=(1/2)
y=(1/2)x-------> in this case the value of y is one-half of the value of x
therefore
the solution is the case c) see the attached figure
