Let's analyze both tables to determine if the values of $x$ and $y$ are proportional, and if so, find the constant of proportionality.

Table 1

We have the following values for $x$ and $y$: $x: 28, 35, 9$ $y: 4, 5, 63$

To check if $x$ and $y$ are proportional, we need to determine if the ratios $\frac{y}{x}$ are constant.

• For $x = 28$ and $y = 4$, the ratio is $\frac{4}{28} = \frac{1}{7}$.
• For $x = 35$ and $y = 5$, the ratio is $\frac{5}{35} = \frac{1}{7}$.
• For $x = 9$ and $y = 63$, the ratio is $\frac{63}{9} = 7$.

Since the ratios are not the same (i.e., $\frac{1}{7}$ and 7), the values of $x$ and $y$ in Table 1 are not proportional.

Table 2

We have the following values for $x$ and $y$: $x: 4, 5, 9$ $y: 8, 15, 36$

Again, we'll check if the ratios $\frac{y}{x}$ are constant.

• For $x = 4$ and $y = 8$, the ratio is $\frac{8}{4} = 2$.
• For $x = 5$ and $y = 15$, the ratio is $\frac{15}{5} = 3$.
• For $x = 9$ and $y = 36$, the ratio is $\frac{36}{9} = 4$.

Since the ratios are not the same (i.e., 2, 3, and 4), the values of $x$ and $y$ in Table 2 are also not proportional.

Summary:

• Table 1: Not proportional
• Table 2: Not proportional

Would you like to dive into any specific part of the analysis or have further questions? Here are some related questions for you to explore:

1. How do we define proportional relationships mathematically?
2. What is the importance of the constant of proportionality?
3. How can we use graphing to check if two quantities are proportional?
4. Can two sets of data still be proportional with varying numbers in them?
5. What are some real-world examples where proportional relationships are used?

Tip: Always check if the ratio $\frac{y}{x}$ is constant for all pairs to determine if two variables are proportional.