Math Problem Statement
Do the two tables show the same proportional relationship between x and y? Explain.
Solution
Let's analyze the problem shown in the image.
The task is to determine if the two tables show the same proportional relationship between and .
First Table:
\begin{aligned} x &= 500, \, 750, \, 1000 \\ y &= 1250, \, 1875, \, 2500 \end{aligned}$$ To check proportionality, calculate the ratio $$\frac{y}{x}$$ for each pair: 1. $$\frac{1250}{500} = 2.5$$ 2. $$\frac{1875}{750} = 2.5$$ 3. $$\frac{2500}{1000} = 2.5$$ Since the ratio $$\frac{y}{x} = 2.5$$ is constant, the first table represents a proportional relationship. --- ### Second Table: $$\text{Values: } \begin{aligned} x &= 3, \, 4, \, 5 \\ y &= 4.2, \, 5.6, \, 7 \end{aligned}$$ Again, calculate $$\frac{y}{x}$$: 1. $$\frac{4.2}{3} = 1.4$$ 2. $$\frac{5.6}{4} = 1.4$$ 3. $$\frac{7}{5} = 1.4$$ The ratio $$\frac{y}{x} = 1.4$$ is also constant, so the second table is proportional as well. --- ### Comparing the Two Tables: The proportional relationships in the two tables are different because their ratios $$\frac{y}{x}$$ differ: - First table: $$\frac{y}{x} = 2.5$$ - Second table: $$\frac{y}{x} = 1.4$$ Thus, the two tables **do not show the same proportional relationship**. --- Would you like a detailed breakdown of proportionality or further clarification? --- ### Related Questions: 1. How do you determine proportionality in tables of values? 2. What are some examples of real-life proportional relationships? 3. How would the graphs of these two proportional relationships differ? 4. How do you test if a relationship is non-proportional? 5. Can proportionality be extended to cases with three or more variables? --- ### Tip: To quickly check proportionality, focus on whether the ratio $$\frac{y}{x}$$ (or $$\frac{x}{y}$$) is constant across all data points!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Proportional Relationships
Ratios
Formulas
y/x (ratio for proportionality)
Theorems
Constant Ratio Theorem for Proportionality
Suitable Grade Level
Grades 6-8