Math Problem Statement
Determine whether each table represents a proportional relationship. If it does, identify the constant of proportionality.
Solution
The problem involves recognizing proportional relationships in tables. Let's analyze each table to determine if they represent a proportional relationship and, if they do, identify the constant of proportionality.
Table 1:
x & y \\ \hline 2 & 18 \\ 5 & 45 \\ 7 & 63 \\ \end{array}$$ To determine if the relationship is proportional, divide $$y$$ by $$x$$ for each pair: 1. $$\frac{y}{x} = \frac{18}{2} = 9$$ 2. $$\frac{y}{x} = \frac{45}{5} = 9$$ 3. $$\frac{y}{x} = \frac{63}{7} = 9$$ Since the ratio $$\frac{y}{x}$$ is constant (always 9), the relationship is proportional. The constant of proportionality is **9**. ### Table 2: $$\begin{array}{c|c} x & y \\ \hline 3 & 42 \\ 4 & 60 \\ 5 & 80 \\ \end{array}$$ Let's check if this table represents a proportional relationship by calculating $$\frac{y}{x}$$: 1. $$\frac{y}{x} = \frac{42}{3} = 14$$ 2. $$\frac{y}{x} = \frac{60}{4} = 15$$ 3. $$\frac{y}{x} = \frac{80}{5} = 16$$ The ratio $$\frac{y}{x}$$ is not constant (14, 15, and 16), so this table **does not** represent a proportional relationship. ### Summary: - **Table 1**: Proportional relationship with a constant of proportionality of **9**. - **Table 2**: Not a proportional relationship. Would you like more details or have any questions? Here are 5 related questions: 1. How can you verify if a table represents a proportional relationship? 2. What does the constant of proportionality represent in a real-world scenario? 3. Can a non-linear relationship be proportional? 4. How do changes in $$x$$ affect $$y$$ in a proportional relationship? 5. What are examples of real-life situations that involve proportional relationships? **Tip:** When checking for proportionality, always look for a consistent ratio between the two variables across all data points.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Proportional Relationships
Ratios
Constant of Proportionality
Formulas
y = kx where k is the constant of proportionality
Theorems
Proportionality Theorem
Suitable Grade Level
Grades 6-8