Answer:
Table C
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
Find the value of the constant of proportionality in each table
Table A
For [tex]x=-2, y=-4[/tex] ------>[tex]k=-4/-2=2[/tex]
For [tex]x=-1, y=-3[/tex] ------>[tex]k=-3/-1=3[/tex]
This table has different values of k
therefore
the table A does not represent a proportional relationship
Table B
For [tex]x=-2, y=-4[/tex] ------>[tex]k=-4/-2=2[/tex]
For [tex]x=-1, y=-2[/tex] ------>[tex]k=-2/-1=2[/tex]
For [tex]x=1, y=3[/tex] ------>[tex]k=3/1=3[/tex]
This table has different values of k
therefore
the table B does not represent a proportional relationship
Table C
For [tex]x=-2, y=-4[/tex] ------>[tex]k=-4/-2=2[/tex]
For [tex]x=-1, y=-2[/tex] ------>[tex]k=-2/-1=2[/tex]
For [tex]x=1, y=2[/tex] ------>[tex]k=2/1=2[/tex]
For [tex]x=2, y=4[/tex] ------>[tex]k=4/2=2[/tex]
This table has the same value of k
therefore
the table C represent a proportional relationship
Table D
For [tex]x=-2, y=-4[/tex] ------>[tex]k=-4/-2=2[/tex]
For [tex]x=-1, y=-2[/tex] ------>[tex]k=-2/-1=2[/tex]
For [tex]x=1, y=2[/tex] ------>[tex]k=2/1=2[/tex]
For [tex]x=2, y=6[/tex] ------>[tex]k=6/2=3[/tex]
This table has different values of k
therefore
the table D does not represent a proportional relationship
