Question

The constant of proportionality is the amount a relationship will change for each unit.

It is represented by the value of this ratio:

k=y/x

One of the ways a proportional relationship is identified is with a table showing the input and output values that change by the same unit rate.



On this table, the pounds of peaches (p) is the input and the cost of the pounds (c) is the output. The constant of proportionality for the table may be determined:

k=y/x = 2.25/1=2.25

All of the ratios on the table are equivalent. 4.5/2=2.25
6.75/3=2.25
9/4=2.25

k = $2.25 per pound of peaches



(4 points)
Determine the constant of proportionality for each table. If the table does not have an constant of proportionality, enter the letter "n" in box.



k = $
per gallon of gas

================================





k = $
per candy bars sold

================================



k =
eggs per batch of sugar cookies

================================





k = $
per pound of bananas

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Answer 1

To determine the constant of proportionality (k) for each scenario, we'll analyze the provided data in each table. Below are examples and calculations for commonly seen situations. Please share the specific data or values from the tables you'd like analyzed for accurate calculations. Without the tables, here's a general approach for how to find the constants of proportionality:

1. **Gallons of Gas (k = $ per gallon):**
- If you have a table with gallons of gas (input) and cost (output), compute k using the formula k = cost/gallons.
- For example, if the cost for 5 gallons is $15, then:
\[
k = \frac{15}{5} = 3 \quad \text{(k = $3 per gallon)}
\]

2. **Candy Bars Sold (k = $ per candy bar):**
- Analyze a table showing the number of candy bars (input) and total cost (output).
- For instance, if 10 bars cost $20, then:
\[
k = \frac{20}{10} = 2 \quad \text{(k = $2 per candy bar)}
\]

3. **Eggs per Batch of Sugar Cookies (k = number of eggs per batch):**
- Look at a table where the number of batches is compared with the number of eggs.
- For example, if 2 batches require 4 eggs:
\[
k = \frac{4}{2} = 2 \quad \text{(k = 2 eggs per batch)}
\]

4. **Pounds of Bananas (k = $ per pound):**
- Similar to the above examples, calculate k using pounds of bananas and total cost.
- For example, if the cost of 3 pounds is $6:
\[
k = \frac{6}{3} = 2 \quad \text{(k = $2 per pound)}
\]

If any tables do not show a consistent rate (proportionality), then insert "n" for that case.

Please provide the actual data values in a similar format as the peach cost for accurate results!