To determine proportional relationships in tables, you can follow these simple steps:
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Identify the Variables: Look at the two columns in your table. Typically, one represents the independent variable (x) and the other the dependent variable (y).
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Calculate Ratios: For each row, calculate the ratio of \( y \) to \( x \) (i.e., \( \frac{y}{x} \)).
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Check for Consistency: If the same ratio is obtained for every row in the table, then \( y \) is proportional to \( x \) (i.e., they have a direct relationship).
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Identify the Constant of Proportionality: If \( y \) is proportional to \( x \), the constant ratio (the result of \( \frac{y}{x} \)) is the constant of proportionality (k). The relationship can be expressed as \( y = kx \).
Quick Example:
| x | y | |---|---| | 1 | 3 | | 2 | 6 | | 3 | 9 | | 4 | 12 |
Step 1: Identify \( x \) and \( y \).
Step 2: Calculate ratios:
- \( \frac{3}{1} = 3 \)
- \( \frac{6}{2} = 3 \)
- \( \frac{9}{3} = 3 \)
- \( \frac{12}{4} = 3 \)
Step 3: Check for consistency: All ratios equal 3.
Step 4: Determine the constant of proportionality: \( k = 3 \).
Thus, the relationship between \( x \) and \( y \) can be expressed as \( y = 3x \).
Summary:
- If the ratios \( \frac{y}{x} \) are consistent across the table, \( y \) is proportional to \( x \).
- The constant ratio is the constant of proportionality.