To determine the equation and the constant of proportionality from the tables or graphs you have, we need some specific data points or values. Since I don’t have access to the actual tables or graphs you're referring to, I can explain the process of how to find the constant of proportionality and the equation.
Steps to determine the constant of proportionality and the equation:
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Identify Points: Look for pairs of values in the tables or points in the graphs that represent the relationship.
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Find the Constant of Proportionality (k):
- Use the formula for constant of proportionality: \[ k = \frac{y}{x} \]
- Select a pair of (x, y) values from the table or graph (preferably multiple pairs to ensure accuracy) and divide y by x to find k. If k is consistent across multiple pairs, you have found your constant of proportionality.
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Write the Equation: Use the found constant of proportionality to write the equation in the form: \[ y = kx \] Substitute the found value of k into the equation.
Example Calculation:
If you find that, for instance, when \( x = 4 \), \( y = 9 \):
- Calculate \( k \): \[ k = \frac{y}{x} = \frac{9}{4} = 2.25 \]
- The equation becomes: \[ y = 2.25x \]
Fill in the Template:
Now you can fill in the blanks for each relationship you analyze, based on the data you have from the tables or graphs. Ensure that for each relationship you determine both the constant of proportionality and the associated equation.
If you provide me with the specific data from the tables or graphs, I’d be able to help you derive those values directly.