Question

The table shows a proportional relationship.

Answer 1

The Given Table is

x : 0    2     4     6

y :  0  9   18   27

$\frac{x}{y}=\frac{2}{9}=\frac{4}{18}=\frac{6}{27}, {\text{Each being equal to}} \frac{2}{9}$

Which shows a proportional relationship.

Now first plotting these points on two dimensional Coordinate  plane, and then finding equation of line using Two point Slope formula.

$\frac{y-0}{x-0}=\frac{9-0}{2-0} \\\\ y=\frac{9}{2}x {\text{Which is given by Two point formula of line , Joining} (x_{1}, y_{1}), (x_{2}, y_{2}) is \\\\ \frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

y= 4.5 x

Answer 2

Y = 4.5 x because 9/2 is 4.5 18/4 is 4.5 and 27/6 is 4.5