Questions and Answers
What is an example of a situation that represents a proportional relationship?
What is an example of a situation that represents a nonproportional relationship?
What equation represents the situation: 'Victoria charges $5 for each bracelet she makes'?
y = 5x
What equation represents the situation: 'Theatre tickets are $5 a person with a $10 service fee'?
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Define a proportional relationship.
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Define a nonproportional relationship.
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What is the constant of proportionality (CoP) in the equation y = kx?
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What is a linear equation?
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What is the constant of proportionality (CoP) in the equation y = -5x?
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What type of relationship is represented by the equation y = 7x?
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What type of relationship is represented by the equation y = 7x - 3?
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In a table, a relationship is proportional if?
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In a table, a relationship is nonproportional if?
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What is the equation for a proportional relationship?
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What indicates that a graph represents a proportional relationship?
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Study Notes
Proportional Relationships
- A proportional relationship is represented by an equation of the form y = mx, where m is the slope or constant of proportionality.
- Key example: Sergio charges $10 an hour for babysitting, representing a direct proportionality.
- Constant of Proportionality (CoP) indicates what is being multiplied; in y = kx, k is CoP.
Nonproportional Relationships
- Nonproportional relationships contain a constant rate of change but do not pass through the origin.
- Example: Sergio charges a flat fee of $5 for travel in addition to his hourly rate, introducing a nonproportional factor.
- The equation for nonproportional relationships typically follows the format y = mx + b, where b is not zero.
Identifying Relationships
- A relationship is proportional if all ratios of y to x are constant.
- When viewing a table, proportional relationships allow for a clear identification of unit rates.
- Nonproportional relationships show varied ratios, making it difficult to identify multiplication factors easily.
Graphical Representation
- A proportional graph is linear and passes through the origin (0,0).
- To assess if a graph shows a proportional relationship, ensure it forms a straight line and includes the origin.
Examples of Relationships
- Equations indicating proportional relationships include y = 7x and y = 5x.
- Nonproportional examples include y = 7x - 3, indicating a constant y-intercept outside zero.
- All proportional manifestations should lack additional terms (e.g., "+ b" where b ≠ 0).
Key Characteristics
- Proportional: No constant added, only multiplication (e.g., y = 1/4x).
- Nonproportional: Can include addition or subtraction like y = x + 2 or y = x - 5.
- Nonlinear relationships do not follow a straight line, lacking a consistent unit rate.
Summary of Terms
- Linear Equation: Forms a straight line when graphed.
- Non-Proportional Graph: Does not pass through the origin, exhibiting variation.
- Unit Rate: The consistent multiplier in proportional relationships.
General Definitions
- Proportional relationships have a straightforward numerical relationship, while nonproportional require additional context for understanding ratios and changes.
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Description
Dive into the concepts of proportional and nonproportional relationships with these flashcards. Each card presents a real-life example or equation related to these mathematical relationships, helping you understand the distinctions clearly.
