It looks like you're working with a problem involving proportional relationships and their corresponding equations. To help you fill out the template for each table and graph, we can summarize the steps to determine the constant of proportionality and the equation.
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Identify the Constant of Proportionality (k): This is the ratio of y to x (k = y/x). It tells you how much y changes for each unit increase in x.
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Form the Equation: Using the constant of proportionality, write the equation in the form \(y = kx\).
Since you haven't provided the specific tables or graphs, I'll outline how to find the values for these placeholders. Here's what you need to do:
Template
- For each relationship (one for each table/graph):
1st Relationship:
- Constant of proportionality: (Calculate the value or refer to the table/graph)
- Equation for this relationship: \(y = kx\) (Plug in the value of k)
2nd Relationship:
- Constant of proportionality:
- Equation for this relationship:
3rd Relationship:
- Constant of proportionality:
- Equation for this relationship:
4th Relationship:
- Constant of proportionality:
- Equation for this relationship:
Example
If you had a table that showed:
| Pounds (x) | Cost (y) | |------------|----------| | 1 | 2.25 | | 2 | 4.50 | | 3 | 6.75 |
You would compute:
- Constant of proportionality (k): \(k = \frac{2.25}{1} = 2.25\)
- Equation: \(y = 2.25x\)
You would then write:
1st Relationship:
- Constant of proportionality: \(2.25\)
- Equation for this relationship: \(y = 2.25x\)
Repeat this process for the other tables/graphs accordingly.
If you have specific numbers from the tables or graphs you want to analyze, feel free to share them, and I can help you compute the correct constants and equations!