Answer:
Table D
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]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
Verify each case
Table A
For x=1, y=3
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=3/1=3[/tex]
For x=2, y=9
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=9/2=4.5[/tex]
the values of k are different
therefore
The table A not represent a direct variation
Table B
For x=1, y=-5
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=-5/1=-5[/tex]
For x=2, y=5
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=5/2=2.5[/tex]
the values of k are different
therefore
The table B not represent a direct variation
Table C
For x=1, y=-18
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=-18/1=-18[/tex]
For x=2, y=-9
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=-9/2=-4.5[/tex]
the values of k are different
therefore
The table A not represent a direct variation
Table D
For x=1, y=4
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=4/1=4[/tex]
For x=2, y=8
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=8/2=4[/tex]
For x=3, y=12
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=12/3=4[/tex]
All the values of k are equal
therefore
The table D represent a direct variation or proportional relationship
The linear equation is [tex]y=4x[/tex]
