Given:
The table of values.
To find:
Whether the given relation in the table is proportional or non proportional.
Solution:
If y is directly proportional to x, then
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
[tex]\dfrac{y}{x}=k[/tex]
Where, k is the constant of proportionality.
It means the ratio of y and x remains same for proportional relation.
From the given table, the points are (10,18), (11,18.6) and (12,19.2). The ratio of y to x for these points are:
[tex]\dfrac{18}{10}=1.8[/tex]
[tex]\dfrac{18.6}{11}\approx 1.69[/tex]
[tex]\dfrac{19.2}{12}=1.6[/tex]
Since the ratio of y to x for the given points are not equal, therefore the given relation is a non proportional relation.