https://file.aiquickdraw.com/mathbot/file/1728186698633ef0xoe21.jpg

To determine if \(x\) and \(y\) are proportional for both tables, we need to calculate the ratio \(\frac{y}{x}\) for each pair of values in the table. If the ratio is constant, \(x\) and \(y\) are proportional. Let's check each table.

### Table 1:
\[
\begin{aligned}
\frac{y}{x} &= \frac{15}{10} = 1.5, \\
\frac{y}{x} &= \frac{24}{16} = 1.5, \\
\frac{y}{x} &= \frac{30}{20} = 1.5, \\
\frac{y}{x} &= \frac{33}{22} = 1.5.
\end{aligned}
\]
Since the ratio \(\frac{y}{x}\) is constant (1.5) for all values in Table 1, \(x\) and \(y\) are proportional in Table 1. The proportional relationship is \( y = 1.5x \).

### Table 2:
\[
\begin{aligned}
\frac{y}{x} &= \frac{12}{9} = 1.\overline{3}, \\
\frac{y}{x} &= \frac{15}{12} = 1.25, \\
\frac{y}{x} &= \frac{18}{15} = 1.2, \\
\frac{y}{x} &= \frac{21}{18} = 1.1667.
\end{aligned}
\]
Since the ratio \(\frac{y}{x}\) is not constant, \(x\) and \(y\) are not proportional in Table 2.

### Final Answers:
- **Table 1**: Proportional, \( y = 1.5x \)
- **Table 2**: Not proportional

Do you want more details or have any questions? Here are some follow-up questions that might help:

1. How can we verify proportionality if the ratio is a decimal?
2. What is the significance of the constant of proportionality?
3. Can proportional relationships be expressed as linear equations?
4. How can you graph proportional relationships?
5. What are some real-life examples of proportional relationships?

**Tip**: When comparing ratios, always simplify them to check if they are consistent across all data points.

For each table, determine whether it shows that x and y are proportional. If x and y are proportional, fill in the blank with a number in simplest form. (Refer to Table 1 and Table 2)

This problem asks students to determine proportional relationships between x and y in given tables by calculating unit rates. Suitable for Grades 6-8, the problem covers ratio calculations and understanding the constant of proportionality.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation