Math Problem Statement
Does this table show a proportional relationship? If so, what is the constant of proportionality?
| x | 3 | 6 | 9 | 12 |
|---|---|---|---|----|
| y | 12 | 24 | 45 | 60 |
Solution
To determine if the table shows a proportional relationship and to find the constant of proportionality, let’s examine the values in the table.
The table values are as follows:
\hline x & 3 & 6 & 9 & 12 \\ y & 12 & 24 & 45 & 60 \\ \hline \end{array}$$ For a proportional relationship, the ratio $$\frac{y}{x}$$ should be constant across all pairs. 1. For $$x = 3$$ and $$y = 12$$: $$\frac{y}{x} = \frac{12}{3} = 4$$. 2. For $$x = 6$$ and $$y = 24$$: $$\frac{y}{x} = \frac{24}{6} = 4$$. 3. For $$x = 9$$ and $$y = 45$$: $$\frac{y}{x} = \frac{45}{9} = 5$$. 4. For $$x = 12$$ and $$y = 60$$: $$\frac{y}{x} = \frac{60}{12} = 5$$. Since the ratio $$\frac{y}{x}$$ is not consistent (it changes from 4 to 5), the values do not form a proportional relationship. **Answer:** The correct choice is: - **No; the quantities are not proportional.** Would you like more details, or do you have any questions? --- Here are 5 related questions to deepen understanding: 1. How can you identify a proportional relationship in a table of values? 2. What are common methods to calculate the constant of proportionality? 3. How do proportional relationships differ from linear relationships? 4. What is the significance of a constant ratio in a proportional relationship? 5. How does one solve for missing values in a proportional relationship? **Tip:** Always check that the ratio remains the same across all pairs when identifying proportional relationships.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Proportional Relationships
Ratios
Constant of Proportionality
Formulas
Constant of proportionality k = y / x
Theorems
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Suitable Grade Level
Grade 7