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 or
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
<u><em>Verify each case</em></u>
<em>Table A</em>
For x=1, y=3
Find the value of k
----->
For x=2, y=9
Find the value of k
----->
the values of k are different
therefore
The table A not represent a direct variation
<em>Table B</em>
For x=1, y=-5
Find the value of k
----->
For x=2, y=5
Find the value of k
----->
the values of k are different
therefore
The table B not represent a direct variation
<em>Table C</em>
For x=1, y=-18
Find the value of k
----->
For x=2, y=-9
Find the value of k
----->
the values of k are different
therefore
The table A not represent a direct variation
<em>Table D</em>
For x=1, y=4
Find the value of k
----->
For x=2, y=8
Find the value of k
----->
For x=3, y=12
Find the value of k
----->
All the values of k are equal
therefore
The table D represent a direct variation or proportional relationship
The linear equation is