We have a table that shows the amount of paint that needed to paint the chairs. The chairs are represented by $x,$ while the amount of paint is represented by $y .$

We know from the previous exercise that the rate of change is constant and equals $\frac{6}{5},$ so this is a linear relationship. In this exercise, we will determine whether the relationship between these two quantities is proportional. To do so, we will express the relationship between the amount of paint and the number of chairs for several rows as a ratio.

Chairs	Cans of Paint	Relationship
$5$	$6$	$\frac{6}{5} = \frac{6}{5}$
$10$	$12$	$\frac{1 2}{1 0} = \frac{6}{5}$
$15$	$18$	$\frac{1 8}{1 5} = \frac{6}{5}$

The ratios of the the amount of paint and the number of chairs are the same. Therefore, the relationship between the two quantities are proportional.

Extra

Further Explanation

Now we will draw the graph of the relationship to show that the relationship is proportional. Therefore, we will write the pairs of the relationship as points.

Next, we will plot the points on the coordinate plane and connect them with a line.

Since the points fall in a straight line, the relationship is linear. Also, the line that we draw passes through the origin, so the relationship is proportional.

Exercise