Math Problem Statement
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)
Solution
To determine if and are proportional for both tables, we need to calculate the ratio for each pair of values in the table. If the ratio is constant, and are proportional. Let's check each table.
Table 1:
\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.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Proportional Relationships
Ratios
Algebra
Formulas
y = kx (where k is the constant of proportionality)
Ratio: y / x
Theorems
Proportionality Theorem
Linear Relationship
Suitable Grade Level
Grades 6-8