A table that represents a proportional relationship will be the one in which every element in y is a constant multiple of the corresponding element in x.
In other words, the points of the table must lie on a line that must pass through the origin.
Let us check each of the tables one by one.
Table 1.
[tex]\frac{11-8}{7-4}=1[/tex]
and
[tex]\frac{14-11}{10-7}=1[/tex]
The difference between the two points is the same BUT every element in y is not a constant multiple of x; therefore, this choice is not correct.
But just to make sure, let us go through other remaining two tables.
[tex]\frac{49-25}{7-5}=12[/tex]
and
[tex]\frac{81-49}{9-7}=16[/tex]
these two slope are not the same; therefore, this is not the right table.
Now for the third table.
[tex]\frac{5-3}{10-6}=0.5[/tex]
and
[tex]\frac{7-5}{14-10}=0.5[/tex]
This table is the correct answer!
Let us now do table 4
[tex]\frac{11-6}{8-3}=1[/tex]
and
[tex]\frac{18-11}{13-8}=\frac{7}{5}[/tex]
the two slopes are not equal; therefore, this table does not represent a proportional relationship.
Hence, the third table is the correct one.
