Additive and Multiplicative Relationships Worksheet
Explore additive and multiplicative relationships with this Grade 10 math worksheet, covering linear equations, growth patterns, and real-world applications.
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Additive and Multiplicative Relationships
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Read each question carefully and determine whether the relationship described is additive, multiplicative, or neither. Provide explanations or calculations where necessary. Show all your work.
1. Which of the following equations represents an additive relationship?
y = 3x
y = x + 5
y = x^2
y = 2/x
2. A recipe calls for 2 cups of flour for every 1 cup of sugar. What type of relationship exists between flour and sugar?
Additive
Multiplicative
Both additive and multiplicative
Neither
3. In an additive relationship, the output is obtained by a constant value to the input.
4. A multiplicative relationship can be represented by the equation y = kx, where k is the .
5. Describe the difference between an additive and a multiplicative relationship in your own words. Provide an example for each.
6. The relationship y = x - 7 is an example of a multiplicative relationship.
True
False
7. If the ratio between two quantities remains constant, their relationship is multiplicative.
True
False
8. Sarah earns $12 per hour. Her friend, Tom, earns $50 plus $8 per hour. Write an equation for each person's earnings (E) based on the number of hours worked (h). Then, determine after how many hours their earnings will be equal.
Sarah's Equation:
Tom's Equation:
Hours when earnings are equal:
9. A plant grows 3 cm every week. It started at a height of 10 cm. Create a table showing the plant's height for the first 5 weeks. Is this an additive or multiplicative relationship? Explain your reasoning.
10. Plot the following points on the coordinate plane and determine if the relationship represented is additive, multiplicative, or neither. Explain your answer.
(0, 2), (1, 4), (2, 6), (3, 8)
Relationship type:
Explanation: