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Understanding the Constant of Proportionality

This worksheet guides you through key concepts of the constant of proportionality, including identification, application, and analysis of proportional relationships in various contexts.

Building a Foundation

1. What is the constant of proportionality in the equation y = 5x? (1 choice)

D) y
C) x
A) 1
B) 5

2. Which of the following statements are true about directly proportional relationships? (multiple choice)

D) The graph can be a curve.
B) The ratio y/x is constant.
A) The graph is a straight line through the origin.
C) The line can have any slope.

3. Explain in your own words what it means for two variables to be directly proportional.

4. Identify the constant of proportionality and the dependent variable in the equation y = 3x.

Constant of Proportionality:

Dependent Variable:

Your answers will be evaluated by AI for key concepts, not exact wording. Focus on main ideas.

Comprehension and Application

5. If the constant of proportionality is 7, what is the equation that represents the relationship between y and x? (1 choice)

C) y = x/7
D) y = 7 + x
B) y = x + 7
A) y = 7x

6. Which of the following graphs could represent a directly proportional relationship? (multiple choice)

A) A line passing through (0,0) with a positive slope.
B) A line passing through (0,0) with a negative slope.
D) A vertical line.
C) A horizontal line.

7. A recipe requires 3 cups of flour for every 2 cups of sugar. Write an equation representing the relationship between flour (f) and sugar (s).

8. If a car travels 60 miles in 1 hour, what is the constant of proportionality between distance and time? (1 choice)

A) 30
B) 60
D) 120
C) 1

Analysis, Evaluation, and Creation

9. Which statement best evaluates the relationship between the variables in the equation y = 10x? (1 choice)

B) y is directly proportional to x with a constant of proportionality of 10.
A) y is inversely proportional to x.
C) y is independent of x.
D) y is directly proportional to x with a constant of proportionality of 1.

10. Create a scenario where the constant of proportionality is 5. Which of the following could be correct? (multiple choice)

C) A book costs $5 each.
B) A factory produces 5 widgets per hour.
A) A taxi charges $5 per mile.
D) A train travels 5 miles per hour.

11. Design a real-world problem involving a directly proportional relationship. Provide the equation and explain how you would solve it.

12. If the graph of a relationship between x and y is a straight line through the origin with a slope of 2, what is the constant of proportionality? (1 choice)

C) 2
A) 0
D) 3
B) 1

13. Which of the following scenarios can be modeled by a directly proportional relationship? (multiple choice)

D) The height of a plant over time with varying growth rates.
B) The temperature in Celsius and Fahrenheit.
C) The number of pages read and time spent reading at a constant speed.
A) The cost of apples is $2 per apple.

14. Analyze the table below and determine if the relationship between x and y is directly proportional. Justify your answer.

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