The problem asks to determine whether the table of values represents a proportional relationship between $x$ and $y$. The table has the following values: $x = 5, y = 16.5$ $x = 11, y = 36.3$ $x = 13, y = 42.9$

1. Problem Description

The problem asks to determine whether the table of values represents a proportional relationship between $x$ and $y$. The table has the following values:

$x = 5, y = 16.5$

$x = 11, y = 36.3$

$x = 13, y = 42.9$

2. Solution Steps

A relationship is proportional if the ratio $\frac{y}{x}$ is constant for all pairs of values in the table. We need to calculate this ratio for each pair:

For the first pair, $\frac{y}{x} = \frac{16.5}{5} = 3.3$

For the second pair, $\frac{y}{x} = \frac{36.3}{11} = 3.3$

For the third pair, $\frac{y}{x} = \frac{42.9}{13} = 3.3$

Since the ratio $\frac{y}{x}$ is the same for all pairs, the relationship is proportional.

3. Final Answer

Proportional