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

Question

It is represented by the value of this ratio:

k=yx

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=yx = 2.251=2.25

All of the ratios on the table are equivalent. 4.52=2.25
6.753=2.25
94=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 in each scenario provided, you need to analyze the relationship between the input (independent variable) and the output (dependent variable). Here's how you can find the constant of proportionality (k) for each situation:

1. Gas Prices: If a table of gas prices is provided that shows, for example, gallons of gas and their corresponding costs, you would compute k by finding the ratio of the total cost to the gallons. For example, if 10 gallons cost $30, then k = 30/10 = 3.00. You would need to insert the data from the table to perform this calculation.

   • k = $ (Cost) per gallon of gas = $3.00 (example); adjust based on actual data from the table

2. Candy Bars: Similar to the gas scenario, if you have a table showing the number of candy bars sold and their corresponding total sales (cost), compute k using the same method. For example, if 5 candy bars were sold for $10, then k = 10/5 = 2.00.

   • k = $ (Cost) per candy bars sold = $2.00 (example); adjust based on actual data from the table

3. Eggs per Batch: For a table that presents the number of eggs used for batches of sugar cookies, the constant of proportionality would be determined by the number of eggs per batch. If 2 batches use 6 eggs, then k = 6/2 = 3.

   • k = (eggs) per batch of sugar cookies = 3 eggs/batch (example); adjust based on actual data from the table

4. Bananas: Similar to gas prices and candy bars, for bananas, if you have a table showing pounds of bananas and the cost, calculate k by finding the ratio (cost per pound). If 4 pounds cost $8, then k = 8/4 = 2.00.

   • k = $ (Cost) per pound of bananas = $2.00 (example); adjust based on actual data from the table

If any of the tables provided do not maintain a consistent ratio, the value for that constant of proportionality would be "n". Without the specific tables to reference, you will need to take the actual values given in your tables to calculate these constants of proportionality accurately.