Math Problem Statement
Is this table proportional or non-proportional?
Solution
To determine if the table is proportional, we need to check if the ratio between corresponding and values is consistent across all pairs.
The table is:
\hline x & 8 & 16 & 24 & 32 \\ \hline y & 2 & 4 & 6 & 8 \\ \hline \end{array}$$ Now, let's calculate the ratio $$\frac{y}{x}$$ for each pair: 1. For $$x = 8$$ and $$y = 2$$: $$\frac{y}{x} = \frac{2}{8} = \frac{1}{4}$$ 2. For $$x = 16$$ and $$y = 4$$: $$\frac{y}{x} = \frac{4}{16} = \frac{1}{4}$$ 3. For $$x = 24$$ and $$y = 6$$: $$\frac{y}{x} = \frac{6}{24} = \frac{1}{4}$$ 4. For $$x = 32$$ and $$y = 8$$: $$\frac{y}{x} = \frac{8}{32} = \frac{1}{4}$$ Since the ratio $$\frac{y}{x}$$ is consistent and equal to $$\frac{1}{4}$$ for all pairs, the relationship is **proportional**. Would you like more details on how to determine proportionality? --- ### Related Questions 1. What are other methods to determine proportionality? 2. How do you identify a non-proportional table? 3. What is the significance of a constant ratio in proportional relationships? 4. Can proportional relationships be represented on a graph? 5. How can proportional relationships be applied in real-life situations? ### Tip Always check all pairs in a table to confirm proportionality, as even a single inconsistency would make it non-proportional.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Ratios
Proportional Relationships
Formulas
Ratio formula y/x
Theorems
Constant Ratio Theorem for Proportionality
Suitable Grade Level
Grade 6-7