Constant Of Proportionality Worksheet Answer Key

Constant of Proportionality Worksheet Answer Key

This worksheet is designed to help students understand the concept of constant of proportionality and how to identify it in various mathematical relationships. Below are the answers to the worksheet.

Section 1: Identifying the Constant of Proportionality

1. In the equation y = 2x, what is the constant of proportionality?

   [📝] Note: The constant of proportionality is the coefficient of the variable term, which is 2 in this case.

   Answer: 2

2. A bakery sells a total of 250 loaves of bread per day. If they sell a constant number of loaves per hour, and they are open for 5 hours, what is the constant of proportionality?

   [📝] Note: To find the constant of proportionality, divide the total number of loaves sold (250) by the number of hours (5).

   Answer: 50

3. In the equation y = 3/4x, what is the constant of proportionality?

   [📝] Note: The constant of proportionality is the coefficient of the variable term, which is ³⁄₄ in this case.

   Answer: ³⁄₄

Section 2: Graphing and Identifying the Constant of Proportionality

1. Graph the equation y = 2x and identify the constant of proportionality.

   [📝] Note: The graph will be a straight line with a slope of 2. The constant of proportionality is the slope of the line.

   Answer: The constant of proportionality is 2.

2. Graph the equation y = 1/2x and identify the constant of proportionality.

   [📝] Note: The graph will be a straight line with a slope of ¹⁄₂. The constant of proportionality is the slope of the line.

   Answer: The constant of proportionality is ¹⁄₂.

Section 3: Writing Equations with a Constant of Proportionality

1. Write an equation in the form y = kx, where k is the constant of proportionality, to represent the relationship between the number of hours worked (x) and the total amount earned (y) if you earn 15 per hour. <p class="pro-note">[📝] Note: The constant of proportionality is the hourly wage, which is 15.

   Answer: y = 15x

2. Write an equation in the form y = kx, where k is the constant of proportionality, to represent the relationship between the number of books sold (x) and the total amount earned (y) if you earn 8 per book. <p class="pro-note">[📝] Note: The constant of proportionality is the price per book, which is 8.

   Answer: y = 8x

Section 4: Real-World Applications

1. A car rental company charges a constant rate of 40 per day plus an additional 0.25 per mile driven. If you rent a car for 3 days and drive a total of 200 miles, what is the total cost?

   [📝] Note: Use the equation y = kx + b, where k is the constant rate per mile and b is the daily rate.

   Answer: y = 0.25x + 120, where x is the number of miles driven. Total cost = 0.25(200) + 120 = 170.

2. A bakery sells a constant number of cupcakes per hour, and they sell a total of 480 cupcakes in 4 hours. If they sell cupcakes for $2 each, what is the total amount earned?

   [📝] Note: Use the equation y = kx, where k is the constant number of cupcakes sold per hour.

   Answer: y = 120x, where x is the number of hours. Total amount earned = 2(480) = 960.

In conclusion, understanding the concept of constant of proportionality is crucial in mathematics and real-world applications. By identifying the constant of proportionality, we can analyze and solve problems involving linear relationships.

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